This is an interesting topic. I will start by saying that without powerlevelling as much as you have (hey, it's your prerogative), we have some life experience in common and seem to have similar views in general on this topic. Anyway, I think you are absolutely correct in that the refusal to use these pronouns is a political statement in itself. I mean, it kind of has to be at this point since discourse has been driven to such extremes.
The story has always been, "Hey, these are preferred pronouns and it would just be really polite to use the pronouns people prefer!" and if it had stayed there, I don't think we would be seeing both sides digging in their heels so hard but we know it didn't stay there. "Preferred pronouns" turned into "demanded pronouns" really quickly and people get really itchy when you start trying to compel speech in them. Then of course, it isn't just speech that is being compelled here, is it? One must also truly believe inside (or at least be a really good actor so no one suspects) that a female who looks like a female or vise versa, is somehow "not" simply on their say so.
There is a set of beliefs being demanded of people, not simply pronouns. Pronouns are merely a trojan horse, not the end game and people are starting to understand that so they are pushing back. I mean, if you are a a gay man or lesbian, for instance, by agreeing to pretend to believe by using peoples asinine "preferred pronouns" is the same as tacitly agreeing that the female penis or male vagina is a thing. Which is the same as tacitly agreeing that your own sexuality is a non-existent entity, which is obviously not a thing that many will want to do for obvious reasons. This extends to straight people too: by using pronouns these days for these "non-binary" idiots, one is tacitly agreeing their very sexuality is non-existent or somehow bigoted. That's a tough fucking sell, but that's what the problem is here. They will not be happy until you submit to their gender religion. So people don't want to. It feels like someone is holding a metaphorical gun to your head like, "SAY IT! SAY IT UNTIL YOU BELIEVE IT!". Of course people will push back on that kind of thing! Who wouldn't? People don't like being tricked into doing things that would be detrimental to themselves.
There's a power struggle going on and it isn't even about pronouns. Nothing the trans community does is above board. Everything is obfuscated by something that sounds a lot nicer. "Preferred pronouns", "genital preferences", blah blah blah. It's always something way darker in reality. So tbh, yeah, fuck using "they/them", I won't do it.