Having thick skin is a good thing. Actively showing off your fragility isn't.
Treating people charitably is a good thing. Actively looking for gotchas isn't.
This is about controlling speech and revisionism, while using sensitive people as an excuse for it. Why? Because it makes you more relevant, if you set the agenda. You get to choose who is good or bad in this absurd moral system where words, not their meaning or your actions, is the basis for judgment. Ironically, this is about good old self-interest and power.
Moralism seems to be inherent in humans, there are always those who self-select to police the behavior of other people. What’s scary with this stuff is that this particular flavor of it has a blind spot (apologies for ableist language, 10 lashes for me) among our current intellectual gate keeping class – most of them just let this pass through and even think it’s a good idea. That’s the only reason this BS can get amplified in influential institutions.