I'm not woke, I consider the intellectual frameworks the Woke operate within to be simply bad. I actually thought of looking for a PBP game to get away from that nonsense, since I've been dealing with woke authors in reading for a dissertation. But when it comes to gaming, take in some perspective, you can choose who you want to play with, if you like me don't want the woke at the table or virtual table, well don't invite them, or leave a disclaimer, if someone whines about it, well tell them directly why you don't want them there, don't use hyperbolic language, don't use insults, just note something like, "I find Woke ideology to be poorly thought out and constructed questionbegging, and it can be particularly tiresome given the tendency of the woke to attempt to psychologize their political opponents or who otherwise seem to argue that they know my mind better than I do. This is no conducive to the rest and relaxation I need right now." Its honest, but not personal, and might provide some food for thought.
When it comes to rule sets and the woke, well, let them play their game, RPGers have often tended to create their own worlds anyway, so even with the DnD Multiverse, you can create your own prime, or use an earlier edition. Some people are stuck on rules, personally, I like the WEG D6, most of my RPG experience is Star Wars, bad experience as a teen with DnD, but I played a bit of MSH once, and Mechwarrior once or twice (at least I think it was Mechwarrior). There are universal systems that can be used as toolboxes for whatever you want, OpenD6, Mutants and Masterminds, someone mentioned Savage worlds, I have no experience with that, but it sounds like it would work, etc. If you are stuck on old school DnD, then you likely already have your materials, and you can send newbies information from retroclones. If not, well, there are free systems, etc., available.
The woke will either escalate into something like the cultural revolution, and neither complaining here, nor arguing with them will change that outcome; or they will burn out on the ultra-left nonsense the same way boomers did when they found the hippie lifestyle didn't work in real life, idealism untempered by realism will often lose because in the end, reality tends to win. Don't get so caught up in the moment's debates that you forget the goal is to have fun, rest, and recharge, and don't forget, some of these movements have been very temporary.