Most people recognize SP as libertarian in general orientation, with a slight liberal bias.
Neither Obama nor Trump has spent a second in office thinking about its portrayal of them.
While I believe Matt & Trey are generally libertarian-leaning I've never detected the slightest bleed-through of libertarian/neoliberal idealism in the show itself.
I've not really watched the show regularly in years, maybe that's changed. I do know that they initially discussed the libertarianism at a time when it was the hip above-it-all precursor to modern both-sides-do-itism that was regularly adopted without much deep reverence to actual libertarianism.
I've never seen South Park as neutral. Its critique of American liberalism is surface level, its critique of American conservatism (whatever that means these days) was fundamental and ideological.
Moreover, I never saw the satire as much more than superficial. Which is fine, I always thought it funny but neither especially acerbic nor intellectual. I think leaning on that "neutral", above-it-all standpoint gave the show some credit that was somewhat undeserved.
I tend to find the degree of depth in South Park is entirely a function of whether you agree with their editorial position and/or whether you've already engaged with that line of thinking elsewhere. (And like every TV show ever, some episodes are good, some are stinkers.)
Why? Because they'll fuck you up? How exactly? Im not asking about presidents' personalities, what would their political friends think? To put it another way, who watches SP, and is it some marginal minority?
Depends on age, mostly: older people on all sides of the spectrum find SP crass. Younger people often think it's funny. You can find overwrought editorials about how SP is problematic/written by cucks, as it offends people on both sides on occasion.
I wouldn't say it's marginal, since everyone's at least heard of it. My general impression is that it tends to be watched by young-to-middle age college educated but middle class people, but you'd have to ask the studio to get a solid demographic breakdown.
Twenty-something college-educated salesmen do. He smokes pot, isn't on welfare, but will also work most of his life.
The intersection of class and education is too broad a topic to discuss in a couple comments, but hopefully that gives you an idea.
I guess this is as good a time as ever to not take freedom of speech for granted, that this concept is seemingly so hard to understand wherever you're from.