I think I would make a clear differentiation between sex and gender/gender identity.
You said your son doesn't think that people can change sex, so he knows that there is a difference between the two. Would he be comfortable with the idea that a transwoman can have a body that is still biologically male, but a female gender identity or feminine gender preferences?
I know that it can be very frustrating to entertain the idea of a gender identity at all (because it's nebulous, badly defined and usually reduces to crude stereotypes). But for kids, "identity" is often about "stuff I like" -- including clothes, music, sports, books, films and peer/friendship groups.
This gets a bit confused when activists compare these fluid, personal identity concepts with a (false) essentialist position that your biological sex determines what you like / are supposed to like. So that if you don't accept the concept of a personal gender identity, you effectively disapprove of people having interests/preferences that don't conform to gendered stereotypes.
If that's where your son is at the moment, he may feel that unless he accepts that a transwoman becomes a biological woman when they transition, that his own exploration of gender is wrong -- and that if you don't completely affirm that TWAW that you disapprove of his choices or are judging him negatively: it feels personal to him.
It sounds like your son has a lot of empathy for people who are not able to express themselves the way they want perhaps because of his experience with his dad getting upset about him using makeup. Maybe one of the things he needs right now, rather than getting in deep on gender theory, is just affirmation that you support him in exploring his clothes/make-up preferences, and that you love him for all parts of who he is not just his gender identity, but all the other things that make him uniquely him.