This is hard, and I'm sorry you're going through that. It's emotionally draining to have an additional source of conflict with your teens. And that's at the best of times. Right now, there's enough pressure on parents and teens even without this subject causing strife.
To be fair, I was more astonished than upset by what my teens came out with after I first took an interest in this subject. My oldest (at the time studying a STEM subject) honestly believed humans could change sex. My middle one told me it didn't cost me anything to be kind to the men claiming womanhood and let them into women's space.
I've never held back on political issues, whether about the insidious effects of poverty, systemic racism or the freedoms we take for granted in the West. I don't hold back now on women's rights either.
I do make sure to listen, I ask lots of questions and explore their reasoning and thinking, and include difficult subjects like male sexual violence, prostitution and the negative impact today's easily available and abundant porn is having on our society. I'm not treading lightly and I know I can't afford to do so - I have sons who need to know this stuff. Two of which are already bigger and much stronger than me and most women, so I explain to them why some women and girls may be scared to encounter them in certain situations where they feel vulnerable and what they could do to avoid that.
I have made progress with my oldest, but my middle keeps trying to catch me out and trip me up (he watches Youtube videos on how to win a debate but simply doesn't have enough experience and knowledge to pull off the easy wins he seeks).
The last apparent gotcha was Do you really think a rapist will wait for the legal right to enter before attacking women in their toilets?
I had a lot of fun answering that one.
And he finally told me that sex is a spectrum of course. Which he tells me he learned in biology at school. That one was fun too.
But my kids love a debate and I've taught them critical thinking from a young age. Plus I stay strictly factual and logical and while they may get annoyed with me, it's not an overly emotional issue for them, (despite having plenty of friends who are full on TWAW, some of whom identify as trans). Which does make coming back from the debate easier.
Above all, when it gets too much, I remind myself of myself at the same age. I gave my mother hell, I believed women's rights were sorted and I knew everything. I definitely knew everything much better than her.