He's doing it by conflating 'priggishness' (puritanical moral conservatism) with a movement that's advocating for equity and trying to dismantle structural oppression. He's deftly sidestepping the power dynamics at play, which fundamentally distinguish these two things. It just so happens that he's in a class of people who sit at the top of a tower of structural advantages benefitting him as he tut-tuts people who are pointing out that they're oppressive to some groups.

Ultimately he's just building a massive wall of text strawman for things he doesn't grasp and attacking it. We're fully in the era of this lazy take, like a dam breaking loose, lots of people who have been threatened by those movements are finally feeling free to attack them en masse.