This quick turn around time doesn't allow the show's creators to stop and worry about who they might offend, but it's pretty evident that they've never cared about that in the first place. South Park is satire, after all. Which means that the show can't go a few years without drumming up some sort of controversy. Most recently, She-Hulk writer, Dana Schwartz, fired off a series of tweets that criticized the program.
Dana lambasted South Park for taking a stance of indifference and claimed that, by distributing their ridicule to each group equally, they've taught viewers that mockery is the correct response to any situation, especially when it comes to politics or social justice issues.
In her thread, she acknowledged that the show isn't directly responsible for it and the onus might be more on fanboys of the program who get off on "intellectual superiority".