Climate change denial. That's the biggest thing for me: they apologized, but it took fifteen years. https://en.wikipedia.org/wiki/ManBearPig

I never jived much with the general nihilism and both/all sides-ism I felt from it, which is probably unfair given it's meant to be a crass comedy.

Not the original commenter, but my guess is because—supposedly—they inspired "kick a ginger day." (Wikipedia) They also pissed off a lot of religious folk by making fun of the absurd beliefs held by various mainstream religions, but I imagine the only people who would take offense to that would be members of said religions who take themselves a bit too seriously.

On the other hand...

• They damaged The Church of Scientology's credibility and demonstrated that it's possible to make fun of that cult without life-ruining retaliation.
• They openly disregarded bomb threats against their creators and the studio to take a stand against groups using threats of violence as a way to silence others.
• They called out the phenomenon of corporations bowing foreign government censorship in exchange for market access.
• Recently, they used a montage sequence to parody how utterly fucked the American healthcare system is.

A lot of their episodes are comedic criticisms of the corrupt institutions in the United States, and they do a good job demonstrating the consequences to people who would otherwise be politically apathetic. But then again, a bunch of people took the wrong messages away and ended up being inspired by Eric Cartman.

It's a mixed bag, but in my opinion, the show has probably done more good than harm.