Yes, and it's in large part because of decades of propaganda, going way back to the days of the Red Scare and McCarthyism early in the Cold War.
In American parlance, many people equate socialism with Marxism and, more specifically, Soviet-style communism, which was nominally based on Marxism. Socialism = communist tyranny is deeply ingrained in much of American political thought. Even though it's been nearly 30 years since the USSR dissolved and even though China (with Vietnam and Laos not too far behind) has long since begun to transition away from a state-owned command economy to a market-based capitalist economy and the Chinese Communist Party quickly becoming communist-in-name-only (though no less authoritarian), red-baiting remains a favorite tactic with many, especially right-wing and libertarian pundits and politicians.
But with no real communist threat on the world stage anymore (aside from North Korea), conservatives' political opponents in America are now deemed to be the new Red Menace threatening freedom and capitalism. Propagandists like Rush Limbaugh and the Fox News pundit squad are constantly trying to frame the Democrats, even centrist corporate Dems, as a horde of literal Stalinists intentionally and maliciously plotting the demise of America and its market economy. Any attempt to critique capitalism's shortcomings is framed as "socialism/Marxism/communism." Things like government-provided services or regulations of private businesses are regarded as a slippery slope leading right down to the front door of a gulag. This year has shown that even things like quarantining or mask-wearing can be framed as literal communism. It's become a knee-jerk reaction to define "socialism" as "anything the government does that I don't like, especially if the Democrats think it's a good idea."
But "socialism" at its core means precisely one thing: public ownership of the means of production. Said public ownership can be indirectly through the state or directly through institutions such as worker co-ops. In its latter form, socialism doesn't even necessarily have to preclude market mechanisms. A completely state-owned command economy is not a prerequisite of socialism. But what counts as part of the means of production? Is state ownership any service "socialism"? Are roads and other public infrastructure, police and emergency services, military forces, public schools, or social insurance and other safety net programs "socialism"?
More importantly, though, does it actually matter whether or not they're socialism? Single-payer healthcare and other programs in other developed nations aimed at benefiting the working class haven't led to Soviet-style communism any more than public roads have. They haven't led to those nations nationalizing their retail stores, restaurants, auto companies, tech companies, movie studios, etc., and they aren't going to. And it won't happen here in America, either.
The Democratic Party as an organization is relatively centrist. It's economic goals have been rather milquetoast for a supposedly "left-leaning" party. Many of its most prominent and mainstream members, including their current presidential nominee, aren't even willing to consider single-payer healthcare or tuition-free college, and are also unwilling to do much that would cause their corporate donors to shy away from them. Forget about wholesale structural changes to our economic institutions. And the supposed "liberal" media are of course owned by massive for-profit corporations who will never allow their employees to advocate for anything that could threaten their business interests. You'll never see an actual socialist hosting a prime time pundit show on CNN or MSNBC, that's for damn sure.
While the party's base has gradually moved to the left, with recent Gallup polls showing that self-identified "liberals" now account for half of all self-identified Democrats (though the Republican party and its base had already moved far to the right when the Democratic base was still overwhelmingly centrist, and continues to move to the right), I would imagine very few of them actually support a totally socialistic economy. And even the most left-leaning Democratic politicians have policy goals that would be noncontroversial in most European nations. Even someone like Bernie Sanders (who's emphatically not a Democrat, even if he ran as one for president) or AOC would be considered bog-standard social democrats outside the U.S. Just because they think rich people should pay a higher tax rate than they currently do or that business should pay their workers a living wage or that we should do something about global warming or that healthcare is a right and not a privilege does not mean they're a bunch of commies out to nationalize Walmart, Apple, Disney, Amazon, Ford, Microsoft, ExxonMobil, Comcast, Wells Fargo, and your local ice cream parlors, hair salons, used record stores, etc. The thought probably never crosses their minds. The idea that the Democrats are somehow literal communists/Marxists/Stalinists/Maoists/whatever-ists is not just factually wrong, it's laughable to the extreme. They are beyond a shadow of a doubt supporters of a primarily market-based economy, with the private sector handling production and distribution of most goods and services.
But whether or not something actually is or is not "socialist" is besides the point with right-wing pundits. It's not nor has it ever been about quaint notions like accurate definitions. The point of propaganda is not to inform. It's to persuade. And more often than not, such persuasion uses intentionally bad-faith arguments and other dishonest means to persuade. To their credit, right-wing propagandists in America have an amazing knack for manipulating language and framing political discourse to serve their own purposes. They've used those skills to achieve two goals: 1) advance the policy goals of the Republican Party, includingbut not limited tosupply-side economics, deregulation of private business, and privatization of public services, and B) make their propaganda itself a profitable enterprise.
Their entire business model is predicated on keeping the GOP base in a state of perpetual outrage against the Democrats. By preying upon decades-old fears of communism, they've been able to convince their loyal listeners that only the Republicans can save them from the horrors of "radical leftist Democrats," and that the only way they can do that is by cutting taxes for the wealthy, gutting environmental protections, demolishing organized labor, and generally making things easier for the Job Creators. They've convinced their audience that what's best for the ultra-wealthy is also what's best for the working class, that any attempt to reign in the excesses of modern capitalism is tantamount to attempting to destroy capitalism, and that the Democrats are literal Marxist socialists with a nefarious left-wing agenda to turn America into a communist state. Even though the pundits' arguments are factually bankrupt, increasingly farcical in nature, and make ever-greater use of baseless conspiracy theories, they work in their intended goal of keeping the conservative base angry. They move the Overton Window further to the right, and their audience follows.
Yes, it is true that every nation with a centralized command economy nominally based on Marxist principles has been an authoritarian single-party state, while every democratic nation has allowed for private ownership of the means of production and has had the private sector comprise the vast majority of its economic output. It's also irrelevant, because not only has the existence of a market-based economy not been a guarantor of freedom and prosperity, but also the goal of the American progressive movement is not to implement a centrally-planned economy, nor to institute a single-party left-wing authoritarian regime. Their goal is to make us more like, well, pretty much every other free and economically-advanced nation. They're thinking Sweden, France, and Germany, not Cuba, Venezuela, or the old USSR. The freest and most prosperous nations have been social democracies, combining a well-regulated market economy with the state providing a strong safety net and certain services (including health insurance and post-secondary education) not effectively allocated by the market.
But the damage to our discourse and our language in general has already been done. Republican politicians and opinion leaders are staunchly opposed to progressive policy proposals because they believe that the government has no business regulating private businesses or providing any sort of social programs to the people (though they are hesitant to outright eliminate popular programs like Social Security and Medicare, which are too popular to eliminate even if conservatives once characterized them as an unacceptable step towards communism), and they have spent considerable money and effort in propagandizing Americans on behalf of an ideology rooted in part in a professed belief in unfettered capitalism. While most Americans do support many prominent progressive policy proposals (alliteration!), such support sometimes depends on how the ideas are being presented. Framing them as "socialism" or "government takeover" gets a more negative response, while more neutral language nets a more positive response. And that's why conservative commentators want people to think of North Korea or Venezuela instead of Norway and Sweden when they hear about those policies.
Most Americans aside from the GOP and their base would be fine with most aspects of social democracy, but many of them really are afraid of anything perceived as "socialist." I'd also say that this is at least part of the reason why Bernie Sanders twice failed to win the Democratic nomination. It wasn't his policy goals, but rather the fact that he flat-out called himself a socialist. Progressives do not need to try to claim "socialism" as a descriptor, because not only is it arguably not accurate, decades of propagandists equating "socialism" with the evils of communist regimes like the USSR have permanently made the term toxic in America, and use of "socialism" as a slur is still useful as a way to make even modest Democratic policy proposals seem absolutely unacceptable even though real-world experience shows social democratic policies are not just benign but beneficial. Unfortunately, messaging often matters more than facts in politics, and the progressive movement has done a far worse job in that regard than the conservatives. By trying to play along with conservatives calling them "socialists" and saying "okay, we're socialists," they'll end up finding themselves even more on the defensive, something the right-wing punditocracy has been doing to them for far too long. The progressive movement needs to do a better job on messaging, to put the right on the defensive for once, and to convince middle America that their goals to adopt programs and policies in place in the rest of the developed world are good for America.