The PC babies are funny because it's human beings doing what we do best, projecting ourselves.
Babies cannot respond to or understand complex dialogue let alone have any credible input on social matters. Their brains aren't developed that far. They cry when they need food or are in discomfort/pick up on what their brains might perceive as a threat. Evolutionary responses. Fight or flight.
So it's completely absurd babies would cry at microaggressions and that's what makes that joke. It's the characters themselves own insecurities or projections onto the babies. Humans often do this with animals as well making great claims their pets understand complex social or political issues.
A little bit of it is just South Park poking whatever fire burns hottest. Like they've always done. Right now it's mentioning anything to do with PC that causes complaining. But heck, even the Catholic Church getting brought up can still get a bit of attention. The guns episode ironically... Very little said.
