The first South Park video game ever actually was on a Nintendo system -- the N64.
It was ported later to the Playstation, but that was the first South Park game and it sold quite well actually.
The South Park creators have also said the current South Park games are inspired in large part to Nintendo's Earthbound (SNES).
Nintendo's policy on content is basically to defer to the ESRB ratings board. If it passes through them, that's generally good enough for Nintendo.
An example of this was that BMXX game on the GameCube back in the day. It had a video clip that had a stripper showing off her boobs. Sony told the publisher they had to censor this or it couldn't release on Playstation 2. Nintendo basically said it passed through the ESRB so they were OK with it. Here's an article about it from back in the day: