To what extent are they?
The notion that the Republican Party is pro-Israel is only partly correct.
Support for Israel has come from both Democratic and Republican politicians. Barack Obama, despite being opposed to Israeli oppression in Palestine, notably said that "Israelis and Palestinians will be better off if Palestinians reject incitement and recognize the legitimacy of Israel." Major donor Haim Saban, who describes himself as a "single-issue" voter on the matter of Israel (and not in the sense of disliking it), has primarily donated to Democratic candidates.
Looking at anti-Semitism, we see a similar pattern, suggesting that the Republican party is not as pro-Jewish as some might be assuming. A Quinnipiac University poll of anti-Semitism found that Republicans were notably less likely to say that it was an issue. Since anti-Semitism is more common among certain far-left groups than the mainstream, it's possible that these results could shift, but it's impossible to say for sure. In any case, at the current time the Republican Party seemingly expresses lower levels of concern for anti-Semitism.
Going further abroad to test the general principle, a survey of anti-Semitism found that Labour supporters were less likely than Conservatives or Liberal Democrats to endorse anti-Semitic statements, as did another survey asking party members whether "Jews' loyalty to Israel made them less British." I believe there was a survey of anti-Semitic incidents that ranked Conservatives below Labour, but Labour below UKIP, but I have not been able to find it.
All of this suggests that the initial impression of the questioner, that the higher level of overall prejudice among Republicans would lend itself to being against Jews as well, isn't totally incorrect.
Nonetheless, it's certainly true that Republicans have been more likely to pursue policies in line with those of Israel's government, such as Donald Trump's support of moving the US embassy to Jerusalem, or Marco Rubio's opposition to the BDS movement, which extended to supporting a bill meant to make it illegal for companies to support them. So, what's going on here?
Evangelical voters have a strong influence in the Republican Party. They represent a quarter of the US population, and are likely a higher percentage of Republicans. Among these evangelical voters, certain groups believe that they have a theological duty to support Israel. As the hugely influential Jerry Falwell said:
To stand against Israel is to stand against God. We believe that. I
love the Jew because God loves the Jew. As a follower of God, I am
under obligation to love as he loves. My life is committed to a number
of priorities, and one of them is to promote, protect, and stand
alongside the Jewish people. History and Scripture prove that God
deals with nations in relation to how they deal with Israel. My deep
conviction is that America will not remain a free nation unless we
defend the freedom of Israel. We must proclaim this from our church
pulpits as ministers, as well as in our daily lives as private
citizens with a Christian obligation to the Jewish people.
Jerry Falwell, The Fundamentalist Phenomenon
Often, this is because they believe that God will return the Jews to Israel before the foretold events of Revelation, as with Pastor John Hagee, who said of the Jewish return to Israel.
God says in Jeremiah 16 — "Behold I will bring them the Jewish people
again unto their land that I gave unto their fathers" — that would be
Abraham, Isaac and Jacob - "Behold I will send for many fishers and
after will I send for many hunters. And they the hunters shall hunt
them" — that will be the Jews — "from every mountain and from every
hill and from out of the holes of the rocks." If that doesn't describe
what Hitler did in the Holocaust — you can't see that. So think about
this — I will send fishers and I will send hunters. A fisher is
someone who entices you with a bait. How many of you know who Theodore
Herzl was? How many of you don't have a clue who he was? Woo, sweet
God! Theodore Herzl is the father of Zionism. He was a Jew that at the
turn of the 19th century said, "this land is our land, God wants us to
live there". So he went to the Jews of Europe and said, "I want you to
come and join me in the land of Israel". So few went, Herzl went into
depression. Those who came founded Israel; those who did not went
through the hell of the Holocaust. Then God sent a hunter. A hunter is
someone who comes with a gun and he forces you. Hitler was a hunter.
And the Bible says — Jeremiah righty? — "they shall hunt them from
every mountain and from every hill and out of the holes of the rocks",
meaning: there's no place to hide. And that will be offensive to some
people. Well, dear heart, be offended: I didn't write it. Jeremiah
wrote it. It was the truth and it is the truth. How did it happen?
Because God allowed it to happen. Why did it happen? Because God said,
"my top priority for the Jewish people is to get them to come back to
the land of Israel". Today Israel is back in the land and they are at
Ezekiel 37 and 8. They are physically alive but they're not
spiritually alive. Now how is God going to cause the Jewish people to
come spiritually alive and say, "the God of Abraham, Isaac and Jacob,
He is God"?
This theology is not pro-Jewish as such, since it comes from a very Christian-centered viewpoint and sometimes espouses anti-Semitic ideas, but it does insist on the centrality of Jewish return to Israel.
Some of these, such as that very John Hagee, were definitely influential on the process.
Netanyahu is betting Israel’s future on people such as Pastor John
Hagee of Christians United for Israel, featured at the ceremony for
Trump’s opening of the Jerusalem embassy. Hagee once said “Hitler was
a hunter” sent by God to drive Jews to Israel. Pro-Israel
apocalypse-minded Christians see Israel as a precursor to the second
coming, when Jews must convert or go to hell.
Further, although most of the Jews in Congress are Democrats, there are conservative Jews among the Republicans in Congress. Jewish people as a whole are more likely to support Israel than non-Jewish people, particularly conservative Jews, so their opinions could have some influence as well.
Bias against Jews is widespread in the United States. But so is bias against Arabs and Muslims, and at the moment, many more-mainstream conservatives see Muslims as the greater threat (among much of the far right, on the other hand, Jews are simply supposed to be behind Muslim immigration, thus seamlessly retaining them as the main foe). As mentioned below, Israel is perceived as opposing Arab and Muslim countries in the region.
Republicans are more likely to express anti-Muslim views, with Trump voters even more likely to hold such beliefs, such as believing that refugees from the Middle East post a threat.
As such, the Republican Party may be somewhat motivated by its anti-Muslim and anti-Arab segment to support Israel as a bulwark against Arab states, as well as to not care too much about its actions toward Palestinians.
Further, more subtle preferences may come into play. Israel's government and culture are more similar to those of the United States than those of Saudi Arabia or Iran. Frequently, defenders of Israel's policies point out that it's the only democracy in the Middle East. The positive aspects of Israel's political system and society have a who section in AIPACs minibook pamphlets. And of course, ethnocentricity is a human universal: people are going to be more sympathetic, on average, to a country whose cultural they identify with more.
Besides, going back to the Evangelical Christian segment of the Republican Party, they've often called themselves Judeo-Christian, which probably increases the perception among their base that Jews (and, by their reasoning, Israel's government) should be supported.
Republicans were, until the election of Trump at least, the party more in favor of free trade. They've also often been more willing to put economic interests ahead of social ones (rightly or wrongly). Even after Trump's election, the priorities of the people currently in Congress have not necessarily changed much.
While Israel is not the largest trading partner of the United States, they nonetheless are pretty far up on the list, at number 24. The vast majority of the countries above it also are pretty high on the "nice list" of the United States, save perhaps for Vietnam, and Saudi Arabia, which despite receiving extensive US support also attracts criticism for its political system and human rights record. As such, Republicans, with their general liking for free trade and great consideration of economic factors, might be less willing to lose a major trading partner by taking a stand against their treatment of Palestinians as harsh as, for instance, was recently taken against Maduro (namely, oil sanctions that will hurt the US economy).
Israel's government is opposed to the government of Iran, and various other Arab governments in the region that have been unsympathetic to US political and military interests in the region. This has been consistent across administrations, with the particular focus on Iran likely owing something to its status as a regional power, potential nuclear capabilities, and frequent inveighing against Israel.
Republicans in the US tend to be foreign policy hawks, save some more isolationist adherents to a more libertarian philosophy. As such, they're more likely to believe in aggressively opposing perceived US enemies, and Israel is seen as a natural ally there.
A note about Trump:
Trump has personally made statements that some have seen as anti-Semitic, such as saying that a primarily Jewish audience wanted to buy politicians. However, more than his own biases, what drives Trump are the people around him in whom he has confidence. He's surrounded by orthodox Republicans, and he mostly pursues their policy priorities. Further, his son-in-law, Jared Kushner, is an observant Jew who has a strong interest in Israel's politics, and has engaged in a lot of work relating to them. As such, his opinions might be a strong influence on those of Trump. The end result is that Trump comes out supporting policies that are in line with those of Israel's current administration, whatever his personal beliefs.