I think it's best explained not by ideology as such, but by self-handicapping. If you're facing a hard exam that you have no idea if you can pass no matter how hard you try, you can study hard, and risk the humiliation of failing... or you can kick back, relax, do a little partying, do a little mildly illegal drugs. Then if you fail, you can say you weren't really trying, you didn't really care that much. And who knows, you might even still succeed, and then you get the satifaction of being so good you didn't even have to work hard!

For a modern Hollywood director, if you put in just a little obnoxiously "woke" stuff, just a pointless gender or race swap, or maybe make someone gay or trans who wasn't in the source material... Now if it fails just for being bad, you can claim it failed because of those handful of people who complained about it online.

So it's not that the "woke lobby" has that much power to force directors to "cast diversely" or something, it's just that it's a convenient excuse for everyone involved. Nobody ever got fired for choosing IBM, and nobody ever got fired for making a film look a bit more like affluent modern America.