The shortest answer I can give, is that Israel and Palestine aren't sports teams. We don't just pick one or the other based on a single issue, or based on how similar they are to us. We look at a wide range of issues and the history as best we can, and in the end, we find the Palestinian arguments to be more compelling. It would be silly to make a decision on the right of one group or another to live and settle in a land based on their record regarding LGBT rights or women's rights. These are also important issues, but do not relate directly to a territorial conflict and the legitimacy, or lack thereof, of each party's claim to the right to live, settle, and self determine in a geographic location.
LGBT rights and Gender Equality
Left wing people generally are pro LGBT rights, and Israel is of course the most friendly nation to LGBT folks in the middle east. It also has a good record for gender equality, something quite rare in the middle east (Assad controlled regions of Syria and Fatah controlled Palestine also have good gender equality laws, but are not good on LGBT rights.
Gender equality and LGBT rights are important to western liberals, and in this regard, the Israelis are better than Palestinians, so having these two common values more closely aligned, why do liberals seem to favor Palestinians over Israelis?
Well, there are other factors and values that liberals hold, where Israel has a pretty indefensible record. Code Pink have coined the term Pink Washing, as using support for LGBT rights as a mask for some pretty terrible policies. Justin Trudeau is an excellent example of this, as is Hillary Clinton and Obama. They have far right, hawkish foreign policies, and have no problem waging war, bombing, invading, overthrowing sovereign governments and a host of other crimes. But they cover up their right wing policies with support of LGBT rights.
The goals of Zionism
Israel does the same thing. The Israeli state was founded via the Zionist movement. The goals of the Zionist movement are usually framed in an innocuous way that few could oppose. The right of Jewish people to self determination and create a national home for the Jewish people. This state was to be both Jewish and democratic. Sounds good? Of course it does! But this framing completely ignores the existence of another people.
Palestinians, Christians and Arabs, who were the majority population. The foundation of a Jewish and democratic state required a Jewish majority in Palestine. And in 1948, even after decades of mass immigration, the Jewish population was still only 33% of the total population.
So how do you create a Jewish and democratic state in a land that is 66% non Jewish? This is the part that Israel's defenders don't like to address. There are two answers, one is mass immigration to bolster the Jewish population, the other is ethnic cleansing of as many Muslims and Christians as possible. And this is what happened. So here comes the first reason: liberals don't like racism, ethnic or religious supremacism, or ethnic cleansing. And these are the foundations of the Israeli state.
Settler Colonial Expansion
Zionism has a goal, explicitly stated among Israelis, but seldom mentioned in western press: Eretz Israel. An Israeli state that encompasses all the land between the Jordanian river and Mediterranean sea. This means that from the beginning, Israeli intended to expand their state into lands designated Palestinian, Syrian, Lebanese and Egyptian. Israel started a war in 1967 in which it expanded into all of these states and lands. Israel claims that this was a pre-emptive war, that it was in danger of being attacked. There is evidence to the contrary, including an admission from Menachem Begin:
The Partition of Palestine is illegal. It will never be recognized
.... Jerusalem was and will for ever be our capital. Eretz Israel will
be restored to the people of Israel. All of it. And for Ever.
Iron Wall, p. 25 & Simha Flapan, p. 32
Israel will not transfer Judea, Samaria, and the Gaza District to any >foreign sovereign authority, [because] of the historic right of
our nation to this land, [and] the needs of our national security,
which demand a capability to defend our State and the lives of our
Iron Wall, p. 356
In June 1967 we again had a choice. The Egyptian army concentrations
in the Sinai approaches do not prove that Nasser was really about to
attack us. We must be honest with ourselves. We decided to attack him.
55 Address by Prime Minister Begin at the National Defense College-
8 August 1982
"In June 1967, we again had a choice. The Egyptian Army concentrations
in the Sinai approaches do not prove that Nasser was really about to
attack us. We must be honest with ourselves. We decided to attack
Another reason for the attack against Egypt is Egypt closed the Straits of Tiran as sea trade route to Israel. The Likud charter expressly states that Israel will never allow a Palestinian state between the Jordanian river and Mediterranean sea. The new Jewish Nation State laws also state the goal of creating illegal Israel colonial settlements on Palestinian lands. This is colonialism. Another reason why liberals do not side with Israel. We generally recognize the genocidal and racist nature of settler colonialism, and thus despite Israel's relatively good LGBT policies, we still do not support Israel.
A state that is created by an immigrant people, who usurped and ethnically cleansed many natives is going to have problems. Unless it kills all the people it wronged, those people are going to fight back. They're going to want to take their homes and lands back, so a powerful military is required in order to dominate neighbors and control the Palestinian population, to ensure they never achieve sufficient military capacity to retake their homeland.
Israel has somehow become the recipient of 4.5 billion dollars of military aid, annually, it is the single biggest recipient of American aid despite being a developed, advanced first world nation. It uses this aid to maintain its military dominance. It is the best equipped army in the middle east, maybe in the world. It also has nuclear hegemony. No other nation in the middle east has nuclear weapons. Israel gets a free pass. We can go into the reasons for this, but powerful lobbying interests as well as American desire to have a friendly military base in the region play a part.
The Palestinians on the other hand, are not allowed to have a military, not allowed to have air defense systems, not allowed to have nuclear weapons or anything like that, leaving them at a permanent military disadvantage. Given the vast gulf in military capabilities, there's not a lot Palestinians can do. Israel on the other hand, can basically do whatever they want. The only restraint is international outrage. Up until now, America has shielded Israel from any sanctions or punitive measures for crimes it has committed (which has necessitated the BDS movement as the only means left to pressure Israel to stop illegal behavior), but if Israel were to commit an outright genocide, even America couldn't shield Israel from the rest of the world. So instead, Israel has this process, where it colonizes the West Bank, demolishes Palestinian homes and villages, replaces them with Jewish settlements, then builds fences and roads around these settlements for the settlements security.
As a consequence, Palestinians have been shepherded into small bantustans. Basically little prisons with limited self autonomy, but with Israel controlling all movement in and out of people, goods and money. The Israeli Jewish settlers, who tend to be fanatical extremists, many from America, live under Israeli civil law, while the Palestinian, Muslim and Christian bantustans live under Israeli military law. This system very closely resembles apartheid, and liberals generally are opposed to apartheid. Right wingers on the other hand, have historically sided with Apartheid, whether it was Thatcher in the UK or Reagan in America. Today right wingers are horrified by the mild land ownership reforms in South Africa to restore a small amount of white colonized and "owned" land to the native African people. Apartheid and indigenous people land ownership has always been a left/right issue.
Siege of Gaza
Then there's the Gaza strip. This was also under apartheid control from 1967 to 2005 when Israel withdrew its 8000 settlers and began laying siege to the city and coastal enclave. The reason was the democratic election of a political party who had declared war against Israel, whose stated goal was the removal of all Jewish people from Palestine, and the restoration of Palestinian Muslims (Hamas doesn't care about Palestinian Christians). This group is far right, very repressive of women's rights and uses terrorism as a tactic in its fight against Israel. Terrorism is a widely employed tactic, its used by America and Israel. All nations really, but the term has been politicized in recent years to exclude Jewish or Christian attacks against civilians. Liberals aren't overly fond of this hypocrisy.
The siege of Gaza has resulted in Hamas firing unguided rockets into Israel, and in the second intifada, bus and suicide bomb attacks, car attacks and stabbings against both armed Israeli soldiers and innocent Israeli civilians. It has also resulted in Israel bombing schools, hospitals, refugee camps, sending military snipers to shoot unarmed protesters and more. Liberals here are not very fond of Hamas, but view the situation through a David and Goliath lens, the vastly disproportionate numbers of deaths of Palestinians, especially civilians and children, compared to Israelis, mostly soldiers has resulted in more sympathy for Palestinians, though no love for Hamas.
Political and media collusion against European and American liberals and Progressives
It doesn't help that liberals see Israelis and Israeli agents as siding with racists, white supremacists and right wing nationalistic parties in Europe and America https://www.aljazeera.com/indepth/opinion/union-israel-european-180716085952930.html. Particularly parties than are strongly anti-Muslim. Israeli agents also fund right wing neo "liberal" and conservative corporatists (Haim Saban and Hillary Clinton, Sheldon Adelson and Trump) and general opposition and hostility to left wing liberals, and "democratic socialists" like Bernie Sanders, Alexandria Ocasio Cortez, Jeremy Corbyn, attempts to criminalize and punish peaceful resistance like Boycott Divest And Sanction, and to intimidate, smear and threaten college kids (Canary Mission). Here an Israeli diplomat (agent) admits to conspiring to "take down" UK MPs. https://www.theguardian.com/uk-news/2017/jan/07/israeli-diplomat-shai-masot-caught-on-camera-plotting-to-take-down-uk-mps . People should be up in arms about this in my opinion. Instead, Labour has just accepted a new definition of ant-semitism that equates criticism of the Israeli state and its policies as anti-semitism. This is 1984, Orwellian stuff...
Right wingers generally think in broader strokes, a lot of people view politics as team sports. We're on team "Judeo Christian values" (aka white European values), they're on team "Islamic Jihad". Liberals tend to have more nuanced views and can support Palestinians while acknowledging that culturally and socially, we have more in common with Israelis. In some ways, Israeli society is absolutely better and more liberal than Palestinian society. But I can't let that whitewash (or rather "pinkwash") colonialism, ethnic cleansing, ethno-religious supremacism, war mongering, apartheid, siege and oppression of Palestinians. And I really don't like the influence of Israeli agents on western governments and mainstream media.
Suppression of Free Speech
Liberals are increasingly concerned with pro Israel groups that attempt to censor and criminalize Palestinian rights activists. Palestinian poets https://www.aljazeera.com/news/2018/07/dareen-tatour-sentenced-months-prison-poem-180731084215893.html and artists https://www.timesofisrael.com/italian-graffiti-artist-arrested-for-mural-of-ahed-tamimi-on-security-barrier/ are arrested. Ocasio Cortez and Cynthia Nixon https://nypost.com/2018/09/09/ny-state-dems-call-cynthia-nixon-anti-semitic-prompting-outrage-denials/ are smeared as anti-Semites. British former MP George Galloway was smeared and assaulted by an Israeli extremist https://www.dailymail.co.uk/news/article-2738230/Attacker-breaks-George-Galloway-s-jaw-street.html (full details not published in print, but explained in his radio show. Jewish journalist Max Blumenthal being banned from giving speeches at German universities https://www.alternet.org/world/why-i-was-censored-talking-about-israel-germany. Son of two Holocaust survivors, Norman Finklestein is banned from Israel, loses his job at the university of Chicago despite being very popular with students and Israeli historians respecting his work https://www.theguardian.com/world/2008/may/26/israelandthepalestinians.usa. Jeremy Corbyn is facing relentless smears https://electronicintifada.net/blogs/asa-winstanley/israel-running-campaign-against-jeremy-corbyn, accusations of anti-Semitism for attending a ceremony for PLO members killed in an Israeli terrorist attack, and for hosting an event where a Holocaust survivor criticized Israel or Holocaust Remembrance day. Ahed Tamimi is banned from leaving the West Bank, unable to attend events in Europe she was invited to https://www.haaretz.com/middle-east-news/palestinians/israel-bans-ahed-tamimi-and-family-from-traveling-abroad-1.6464439. Hurricane Maria victims in parts of Texas who support BDS are not eligible for aid for reconstruction of their homes https://forward.com/fast-forward/385628/houston-suburb-wont-give-hurricane-relief-to-bds-supporters/. Attempts in New York make it illegal for the city to do business with BDS supporters https://www.newyorker.com/news/news-desk/cuomo-and-b-d-s-can-new-york-state-boycott-a-boycott. Facebook taking down Palestinian activist profiles at Israels request, criticism of Israel to be banned and on college campuses https://electronicintifada.net/blogs/nora-barrows-friedman/trump-administration-moves-curb-campus-criticism-israel. Left wing folks find this kind of thing quite disturbing, as is the sight of US presidential candidates and politicians swearing loyalty to Israel at AIPAC events every election cycle (they don't do this for any other country). There's a lot of very disturbing political collusion and corruption, as well as censorship and media smear campaigns against Palestinian rights activists. Even if you're a hardcore, died in the wool Israel fan, who believes that Israel should be above criticism and Palestinians are the cause of the problems, these things should be of concern to you if you oppose government and media censorship of free speech and protests.
Religion and Morals
Lastly, the left tends to be less religious than the right, so Biblical promises don't move them as much. They also tend to be more interested in justice and fairness (human rights, animal rights, the environment, indigenous peoples, immigrants etc). As to why these same left wing people don't seem to be so sympathetic to Israelis, particularly the Mizrahi Israelis of Arab origin who have experienced ethnic cleansing, and the European Israelis descended from Holocaust survivors, it probably is because two wrongs don't make a right. The ethnic cleansing of Mizrahi Jews in Jordan, and genocide European Ashkenazi Jews in Europe, does not justify what the Jewish settlers have done to the Palestinians. Over decades of ethnic cleansing, apartheid, siege and massacres, and the very obvious injustice of it all, a lot of people just have lost sympathy for Israelis. The bullied became the bully. When I was a kid in school, and 9/11 happened, I felt very bad for Americans. Everyone did. And then America invaded Afghanistan, and then Iraq, and I started to news stories about Iraqi kids with their arms, eyes and legs blown off by American bombs, and whose family were killed. Then the oil for food program, no WMDs were found... My sympathy was lost, and now when I think if 9/11, it's very difficult to sympathize with Americam even though I know that the people who died that day had nothing to do with those events. Now I just think about all the bad things that were done, and how 9/11 was abused to justify what I would deem to be colonial invasions and illegal wars. I think a lot of people feel the same way about Israel. They may once have had sympathy, but it's gone now, spent, due to the terrible things they've done... It doesn't help that Israelis have weaponised and abused the legacy of the Holocaust in a smear campaign against Palestinians and their supporters, such as Natanyhu defending Hitler and blaming a Palestinian man for the Holocaust. https://youtu.be/-Ju1w-iDR0o So as a result of these factors, a lot of people who would otherwise be very sympathetic with Israeli people's various histories, have lost their sympathy.