Unfortunately what I really think is happening/happened with "woke hate" is manipulation for political gain as you mentioned with propaganda.

These people couldn't care less before, other than the religious zealots that would crusade against anything "gay." The political right (I really believe this started in earnest in the US) found a pressure point to use that puts them in direct opposition to what their political adversary aims to achieve (acceptance of all people for who they are). As it stands in the US the right operates almost entirely based off of "whatever the left aims for, make it appear evil. Always oppose all that they do." as opposed to having specific goals of their own other than "shower the wealthy with benefits, remove all barriers to retaining the entirety of profits."

Steve Bannon recently aimed their manipulation at what he described as "rootless white men" through the lense of gaming and societys affect on games/movies. Ever since that started there's been an "explosion" of "this game woke?" discussions in Steam discussion fourms and in regard to movies. Before this manipulation these people just wouldn't care and if anything you'd just see the odd person here or there complain about 2 guys kissing in a specific scene or something. They are made to be even more angry now because they're made to believe it's an affront to them and an attempt to manipulate them and society... Which is "funny" because they are being manipulated, just not by gaming/movie media.