In all honesty, most people that hate current trek don't hate it because it's too woke, they hate it because it's just generic trash. Classic trek didn't care much about big space battles, loads of pew pew and great action shots. Classic trek cared about great stories. The ships were places where people actually worked and lived together.
Current trek (anything after enterprise) has horrible story lines, horrible dialogue, is mostly about dump action pew pew and CGI, ignores 50 years of history, is all about fuck this, fuck that and fucking fuck you and honestly: it isn't woke: it's only virtue signalling.
Classic trek was woke by making great stories about real issues in society. New trek is just a sad shadow of what it used to be.
I was never bothered by new trek being too woke because it isn't.
To quote a really shitty show: sheer fucking hubris.