"culture wars" is such a nonsense and biased phrase to be using. There are no "culture wars" - there are just biggots being biggots. "war on woke" and "culture wars" and just stupid phrases used by the right wing nutters to try and legitimise there stupidity as some kind of "movement".
Push back for sure, but we should also be reframing the converstion - there is no "war"; this is pushing back against biggotry which is nothing new.