I think your analysis in pretty on point. In my circles, we call this problem "gender essentialism." I see that it stems from neoplatonic thought as derived from Christian puritanism, and it desperately attempts to reconcile a kind of cherry-picked modernism with traditionalism. And it fuckin' sucks.
Transfemme enby here. I hear what you two mean, but I wanna make sure we also resist medicalizing gender nonconformity. While many trans folks undergo bottom surgery to alleviate dysphoria or to simply be "safe" from the scrutiny of the cis gaze, surgery is not what qualifies a trans woman as a woman. The issue isn't about genitalia, it's about transmisogyny.
TERFs have so deeply internalized the misogyny that it's all they know, woman TERFs and man TERFs alike, cis or not ('cause Caitlyn Jenner is still a TERF).
This may be the most Dutch thing I've ever heard. (I'm Dutch.)
I think the most effective method is to do some sort of organized boycott. We all know well enough how sheisty these companies are. Time to start encouraging each other to quit them en masse.