Bernie Sanders is called "radical socialist" or even "communist" in America but in Europe, as I understand it, he would be considered a center-left or even centrist politician. Europe also participated in the Cold War against the Soviet socialist regime, but they managed not to develop a strong aversion to anything that involves higher taxes, more regulation, free healthcare (or state-run and, therefore, cheaper healthcare), etc. For example, in the UK, the Tories not only don't call NHS "radical left socialism", but they are instead pretty vociferous in their demands to fund it more (including by diverting EU-bound £350m — at least, according to the Brexit campaign's not-entirely-accurate allegation; the campaign was spearheaded, in large part, by now-prime minister from the Conservative Party Boris Johnson). How come?
(This answer assumes right-wing as in: individualist / small-government / pro-business, not right-wing as in authoritarian or royalist)
This has to do with the history of the USA. A complete answer would take an entire book, so this answer is not complete, but two important contributing factors for Americans with a protestant white European migration history are:
Manifest destiny has contributed to a culture of individualism in the USA. For much of US history, immigrants were getting free plots of land in the west. It was up to them to build a house and defend themselves against any natives who might disagree on who has the right to use this land. People very much depended on themselves only, and may view the government as being in the way rather than being a source of help. Much of the Mid-Western United States was settled this way, and rural areas here remain very much Republican Party strongholds.
Compare this to Canada, where the Royal Canadian Mounted Police (RCMP), or mounties, would go ahead and pacify areas ahead of migrants settling there. It may have been considered more civil, but was certainly a more collective approach. You'll notice that politically, Canada is in some ways more like European countries than like the USA. They still have a Queen too.
The social-democratic, socialist, or communist movement is inherently collective in nature, and based on the idea (I'm oversimplifying here) that the rich are exploiting the poor. When you have tenant farmers or factory workers, the idea that the rich are exploiting the poor has a good audience (and perhaps indeed some truth), in particular if the rich were born rich and powerful. In Europe, the nobility was still holding most of the power until the early 20th century, when revolutions in some countries and reforms in others took away most of their formal powers. In America, such nobility does not historically exist in the same form. (I don't know how it was in Canada). That's not to say classes don't exist, but the cultural perception is that there is more social mobility, and this was probably true for white men before European countries became democracies and established their welfare states. When the cultural perception is one of more social mobility, people may consider that people who are rich have deserved it. Even many poor Americans still embrace this idea today and have therefore been much less susceptible of leftist ideas.
You'll also find that the cities are more left-wing than rural areas. Although this is partially (but not universally) true in Europe too, I think it's stronger in the US.
Until the early 20th century or so, the USA had a greater freedom of religion than Europe. Many Europeans with religious views that were out of the norms moved to the USA, because they felt they could practice their interpretation of religion there in more freedom. People who are deeply religious are often less susceptible to socialist and communist ideas; Marx was quite critical of (organised) religion, and churches have historically often preached against left-wing movements. Marxists will say this is a ploy to keep people ignorant and prevent them from rising up against their oppressors, but either way, it means left-wing movements have less of a chance. There are still religious conservatives moving to the USA today, because it offers more homeschooling opportunities than many European countries, and for religious reasons, they want to teach their children themselves rather than to subject them to the public education system (where they may be exposed to ideas that the parents strongly disapprove of).
McCathryism and the Red Scare
This was mentioned by Italian Philosophers 4 Monica in a comment.
Propaganda poster, New York Evening Telegram, 1919.
From the Communist Revolution until well after World War II, anti-communism was a strong force in the USA. This was not limited to combating actual communists, but a lot of less radical left-wing movements were accused of communism at all. Even today, people who are not at all communists are accused of communism (example one, example two). To what degree this is cause and to what degree effect of the US being politically right-wing I'm not sure, but it may well be both.
Americans with a different migration history than the White Anglo-Saxon Protestant (WASP) Euro-Americans are not nearly as right-wing. People with a migration path via Latin-America (Hispanic Americans), or with ancestors in Africa (African Americans, often with a history of slavery) are much more likely to vote for the Democratic Party, which currently hosts political ideas to the left compared to the Republican Party (many of them also migrated well after the Red Scare was at its height). Native Americans also largely vote for the Democratic Party, but they are too small in number to be an important political factor nationally. I'm less sure about Asian-Americans but I believe those are largely urban anyway. The trend of minorities more likely voting Democrat is so strong that some describe the Democratic Party as one of minorities.
(The question can be asked how left-wing the Democratic Party is. It's a different question. It seems to me that although the mainstream Democratic Party of the last 20–30 years would be right-of-centre in most European countries, there are some representatives such as Alexandria Ocasio-Cortez whose political positions would be left-of-centre even in Europe; the electoral system of the USA favours a wider variety of opinions in the same party. A similar trend can be seen in the UK, where everyone from Tony Blair to Derek Hatton) is in the same party)
Disclaimer: This is my personal view from the outside (Germany). My only insight is the US news media, which I followed for a few years.
This is difficult to answer, but it all comes down to the two party system, necessitated by the electoral system of the US.
It is easy to say "no" to change and it's easy to get people to say "no", but it's difficult to enact change, because change is, emotionally, difficult to predict and scary, so political actors that are against change have significantly more power than those that push for change.
As an example, the NRA has one modus operandi: Get people to reject every gun law. No discourse or weighing of arguments, just a flat "no", whatever the law might be. There are many such direct or indirect political actors in the US which push for strict rejection of anything that interferes with their status quo. Those political actors are usually aligned closer to parts historically belonging to the republican party, e.g. the climate change deniers (Oil industry saying "no" to regulations), gun proponents (gun lobby saying "no" to gun laws) or trickle down economists (Rich people saying "no" to taxes on them).
This gave the republican party enough power to prevent change when they weren't in charge and enacting their own policies when they were in charge. While the democrats often push arguments, the republicans just as often push flat out rejection.
Those republicans that disagree with those "naysayers" still disagree with the democrats even more on other policy points, so they can't leave their party without leaving politics completely, because forming a new party is all but impossible with the electoral system as is, which forces them to cooperate with the naysayers, giving those even more weight.
This isn't to say that it's entirely the republicans fault. The democratic party does have naysayers as well, especially where party internal change is concerned. Democratic politicians that push for too much change, a reform of the democratic party or even a reform of the electoral system, which would potentially take power away from both established parties, are opposed by democrats that reject change. However, in the last 20-30 years the trend was consistent with democrats pushing for change and republicans rejecting it.
I read an interesting article some years back (unfortunately I cannot locate it at the moment), which held that up until the early 20th century the US privileged economic adventurism: a semi-colonial expansion that took us across the western breadth of the nation, up to Alaska, and out to Hawaii, the Philippines, and other pacific island territories and protectorates. In this period the power of the government was more or less aligned with the interests of individualist capitalism: everything from homesteaders to gold miners to remote plantation owners. As people expanded outward to exploit new resources in comparatively untouched lands, the US army and navy would follow to secure the land, suppress native populations, and guarantee a comparatively safe environment for commercial extraction. However, at the time of the Great Depression the US Government shifted focus. Instead of supporting economic adventurism — which was (after all) complicit in creating the great depression, and which in any case was running out of new territories to expand into — it turned to public assistance and support for people who were not property owners or adventure capitalists, implementing the 'socialist' policies of the New Deal and eventually other 'liberal' institutions.
This shift fostered the political divide we see today. On one side we have 'Rightists' who still follow the capitalist 'colonial adventurism' paradigm. This is a competitive model in which people who fail to secure or use property have no one to blame but themselves, and are undeserving of public assistance; as Weber pointed out, this is aligned with the Protestant (Calvinist) presumption that material success correlates with moral worth, and poverty with moral depravity. Immigrants, indigenous peoples, ethnic minorities, and lower-class laborers are all considered necessary evils: useful for immediate productive purposes, perhaps, but dispensable at the end of their usefulness, and decidedly not qualified to engage in public affairs.
On the other side are the 'Leftists', who see the US as an inclusive multicultural melting pot, and generally object to monopolistic, exploitive economic practices that harm one class of people for the exclusive benefit of another class. Even in the 19th century this group showed up as abolitionists, social reformers, and the like, but by the time of the New Deal they had crystalized as what we would call these days 'social democrats', a blend of liberal and Marxist thinking that emphasized universal rights, broad suffrage, fair wages, social safety nets, judicial and criminal reforms, and other guarantees that individuals are not deprived of certain basic rights merely be cause of social class or wealth.
The exact nature of this divide has shifted over the decades: the Right has moved through segregationism, McCarthyism, masculinism, and the militia mindset to the modern anti-immigrant, anti-islamist standard; the Left moved through civil rights, feminism, gay rights to the general progressive focus on a fair political playing field we see forming today. But the divide has always been a matter of governmental priorities — a dispute over how and to whom government funds should be allocated — and because of a variety of factors has become increasingly polarized.
The impression that the US is 'Rightist' is more a factor of this polarization than a factual reality. Polls consistently show that Americans are largely in favor of many slightly-left-of-center policies; there is broad support in the populace for universal health care, gay marriage, reasonable immigration policies, etc. The US is a bit to the right of Europe because the US has a much stronger Christian community, and religious communities tend to be more socially conservative. But the difference is not as significant as it might seem from listening to US political figures. US politics has been dominated in recent years by people eon the far right of the spectrum, beginning with the creation of FOX News back in the Clinton era and coming to a head with the election of Obama in 2008.
Sanders is a particular target for this 'economic adventurism' Right because he explicitly and openly endorses socialist policies. Even granting that Sander's brand of democratic socialism is milquetoast by European standards — Marxists would see him as a liberal democrat with pretensions to socialist thought — the Right has spent decades vilifying and demonizing socialism in order to shift government policy back to their worldview, and Sanders presents an in-your-face challenge to that news-cycle hegemony. Even the DNC is worried about this, mind you, because that knee-jerk McCarthyist reaction is going to cause some bad optics, and they are not sure they can spin it in their favor. But in any case, I would take this reaction to Sanders less as a reflection of the views of the US populace than as a comment on this long-term, polarized divide among political influencers.
Established parties are more likely to be conservative than radical. If a system works, conservatives do not like to tear it down for ideological reasons. An European right-wing party may oppose free education and public healthcare for ideological reasons while simultaneously supporting them for practical reasons. US democrats may like free education and public healthcare in principle, but they do not actively advocate for them, because the existing system already works. Because the parties are conservative and operate in different environments, it is difficult to say which of them is further to the right.
(Europe has things like free education and public healthcare largely for historical reasons. Revolutionary communists had mainstream appeal, and supporting the demands of the moderate left was seen as a good way to make communism less popular.)
European left-wing parties rarely enjoy majority support (even if we include green parties with the left), while US democrats often do. Democrats often try to appeal to centrist voters in order to win first-past-the-post elections. For these reasons alone, the Democratic Party would not be a left-wing party by European standards, even if there were no fundamental differences between European and US voters.
Voter turnout is another major difference. Highly educated wealthy people are more likely vote than those with low incomes and little education. Politics in countries with low voter turnouts are more likely to be skewed towards the interests of the well-off. In the US, the turnout is usually ~60% in presidential elections and ~40% in midterm elections, while many European countries frequently see 70%, 80%, or even 90% turnouts.
As for Sanders, calling him a radical socialist is appropriate. He is a socialist according to the US usage of the word, he calls himself a socialist, and he certainly advocates for radical changes in the society.
A "trick" theory-answer: perhaps the US is not that politically right-wing, and is, (relative to appearances), more moderate and left wing, but its wealthy conservative elites labor mightily at pretending to make it seem as though the US were right-wing, via quite excellent propaganda disseminated by their majority share of the mass media, as well as longstanding and shameful methods of disenfranchisement and voter suppression.
As to why the US's wealthy conservative elites choose to live this way, perhaps it's because that's how prior generations of wealthy conservatives behaved, and those ruthless traditions are all they believe they can trust.