"Sometimes when people are uncomfortable, they use the Bible as a weapon to try and hurt other people. There's nothing in the Bible that says people can't be trans, but it does say a lot about talking bad about people behind their back.
I know you're uncomfortable with this. I am too, a little. But I'm also happy, and I wasn't happy for a really long time. The Bible does say that God loves us and wants us to be happy, doesn't it? I know I don't look like exactly like a woman, but do you think we should judge people by the way they look? If you're in school with a girl and she's maybe not the prettiest, or she's flat chested, or maybe she's even got zits and big teeth, are you going to tell her she's not a girl? No, that would be really mean, and God wants us to be nice to each other. It's what He sent Jesus to tell us.
I'm the same person you've always known, I'm just happy now. Your mom is upset and doesn't understand, so she doesn't want you to be happy for me or try to understand it, either. Sometimes grown-ups don't handle things any better than kids do, and sometimes they try and use kids against each other. I'm not going to say anything bad about your mom, not now and not ever. But I'm going to talk to her, because she shouldn't be bad-mouthing me either. It's not nice, and it's not right."