A recent example of the media taking South Park a little too seriously is this moment from Season 18. Following the boys' promise of an appearance by Lorde at their party, they're expected to deliver. With no Lorde available, Randy decides to take it upon himself to perform.
What seemed to be just a throwaway gag became something more once a highly-shared article from Spin criticized the show for what they deemed to be an insulting gag. In response, the site actually unintentionally created a massive subplot running through the entirety of the season in which Randy Marsh became Lorde. And due to the new structuring of the episodes where each episode tells a part of a continuous story, this subplot became more relevant than anyone likely expected.
Spin were good sports after the situation, acknowledging that they likely overreacted to what was just a minor sight gag. However, it's not difficult to see how South Park dedicating an entire season to a single article from their site likely was a bit embarrassing, even though the plotline actually yielded plenty of quality (and surprisingly heartfelt) moments at certain points. If there's something to appreciate about SP, it's that strong unpredictability.