"Why should gender matter?"
I just about cried when I saw that. If your mother woke up one morning with everyone calling her "he" and "sir" despite who she really is (or if the analogous event happened to your dad), then I suspect that gender would suddenly matter a whole heck of a lot.
I feel that, as a couple of other people have said, it's fundamentally about who you are, not what you like to do or wear.
Forgive me for being blunt, but your mother sounds hypocritical and ignorant. (Well, you yourself said they were ignorant.) Does she require evidence that someone is being oppressed by demons? If so, what evidence will satisfy her? If not, why does she require evidence that you are a boy?
Sorry, I'm just rambling and not making a heck of a lot of sense.
I have never had to deal with this scenario. I have not been in touch with my own parents for many years. I came out to my brother several months ago and had no real problems. My ex knew I was male-identified since the very early stages of our relationship. The people who didn't know tended to be liberal academics, so no problem when I came back out of the closet.
I have never had to justify my gender to anyone, and (perhaps irrationally), I am offended by the very idea, just as I would be if some well-meaning acquaintance were to ask me, "Gee, how do you know you are a secular humanist? Maybe you really aren't!" or "How do you know that you're gay? Why does it matter? Maybe you're really straight but confused!" It just seems obvious to me. This is who I am, this is what I believe, I didn't arrive there capriciously, take me as I am.
However, other people can't go inside my mind and see what is there. I guess it's reasonable to ask why you think you're a guy. And it's reasonable to feel that the response "Because I identify as one" or "Because I feel like one" is not a very satisfying or convincing answer.
If your parents are willing to do some reading, perhaps a couple of good trans autobiographies would help. Find a book or two that you like that seems to speak of an experience like yours. Then pass it along. But don't be surprised if there isn't much effect.
A therapist should be able to help. Have you started going? Do your parents support the idea? What's up with that?
Sorry if I'm not much help.