This movement is particularly insidious and terrifying because it inserts a wedge between children and their parents. Historically there are many movements that have done that, and they are not good ones.
He probably cannot hear you, because, as @DaisysChains above said, he is male. And young.
My ds is all over "be kind" - he seems to need to support/protect his (vulnerable) trans friends rather than his mother. Which is painful. It hurts when I am seen as the enemy even though he acknowledges that I have always welcomed, supported and accepted him and all his friends just as they are.
I avoid the subject, but it is he who brings it up. This is odd - it obviously bothers him - and I wish we didn't have this (the only subject) which is a difficulty between us in our relationship. However I have lived my woman's life, I know how being a girl and then a woman has shaped all my experiences, and I cannot change that because he wants me to, however much I love him.
Arguing didn't work. When I tried it to start with, his reaction was surprisingly emotional and over the top. It was more like a toddler's, and I think that is because the cognitive dissonance is just too much to cope with.
JKR is transphobic even though he has never read what she has written. Etc etc. It makes no sense. He has a higher degree, and in no other area of his life would he believe things without looking at the evidence. And yes, I did point that out (see previous para!).
The only thing that has cut through is sport. Even he sees that is unfair (did I mention he is male?).
Other than that, when he brings the subject up, I either just ask a question and then leave it, or explain how it affects me personally from my own experience of men and then leave it.
The things that he has gone quiet on include:
Me explaining why I would not be able to undress in front of a stranger with a male body, no matter how they identified.
Asking him why women's spaces were created in the first place. Saying that I hope his female friends don't ever have the kind of experiences at the hands of men that would make them realise why they need them - fighting fire with fire.
The unfairness that results. That to have eg three outdoor ponds in London where people with male bodies can now use all of them but many women (religion/culture/sexual abuse history) can't use any seems really unfair, even though women themselves set up their own pool a hundred or so years ago.
Simply saying that women and girls should be allowed to have their own spaces/sports/boundaries if they want them and we can't give away consent on behalf of others.
Sorry it's an essay.