The way South Park employs xenophobic/racist/sexist tropes is interesting - they are either so silly that its really hard for anyone to take offense, or they spread it around so much - no one group is ever singled out - and no one group is ever spared. That gives us all permission to laugh at them, and laugh at ourselves, when the time comes.
Or... the portrayal isn't actually targeting group of the character embodying the trope. It's targeting those that hold such tropes, in a way that exposes the absurdity of them.
There was a movie few years ago, Tropic Thunder. Robert Downy Jr is in black-face the entire movie, and it's hilarious - and somehow he isn't cancelled. Why? His character in the movie is a white, self-serious method actor (he stays in character all the time), who had medical treatments to alter the pigment of his skin in order to portray the African-American lead in a movie. And his depiction is one giant super charged trope. But the actual butt of the joke isn't black people - its actually the pretentious actors and Hollywood in general. In essence, its making a statement about the absurdity, self-importance, actors, studios, etc in Hollywood, and the lack of the social justice and equality there.
South Park wields "*ist" tropes in a similar way, and I think its incorrect to think of it as racism, or xenophobia, etc.
In South Park, there's one black character in the cast, and his name is Token. As in the token black kid. Out of context, and on its face, it might seem racist. But its saying something else, just like RDJ's role in Tropic Thunder.