I had, still sort of have, something sort of like gender identity disorder.
I guess it wasn't true gender identity disorder because I didn't insist on being called a boy, or become transsexual (but was/am mistaken for a guy sometimes), but I had big problems with gender, and some problems with my sex. I guess I had/have a huge case of strong tomboyness, and hated going thru puberty, hated my body, and I hated everything girl about me, and everything girlish/womanly that was expected of me, and refused to act feminine.
Some people at the church my family went to were sure I was lesbian, and they were bothering me about it, and telling me I would go to hell if I didn't change my ways and repent. Even being a tomboy was bad in their views. During that time I hated going to church, people kept bringing it up and bothering me about it, and I was forced to dress up to the services. It made me feel so sick, all of it. Good thing, my family did not react as harshly, but they were against me being such a rebel. They sometimes approached me about my rebellion against being feminine and the feminine roles I ought to embrace. What my family did hurt too, but not as harsh as what happened from the church members who kept approaching me.
I haven't changed a whole lot. I mostly learned to grudgingly tolerate my female body, and I am still very tomboy and mostly neglect being feminine to the maximum I can get away with. I am sort of weakly androgynous, meaning the androgyny is weakly gendered, and I am somewhat masculine, I guess, but not strongly so.
I don't know how to help you with your family, and I can hardly use Facebook and I hate going to that website. What I would do if it were me is try to avoid the subject of gender, and talk to her about other things if possible. If she insisted on talking about it, I might say It is hard to give up my tomboyness, it is a part of me. I know there is a belief with some people that all tomboys or people with gender dysphoria are gay, but that is not true. Maybe a lot or some are, but not all of them. I don't understand why that is so hard to comprehend. Besides, even if you are gay, people should get over it. It's your life and your issue not theirs.
I don't have any other ideas. Hopefully there are better options.
I don't know if that would really help in your situation, because I really am not wise with understanding people or negotiating issues of their nit-picks, especially nit-picks over gender.
If she decided to cut you out of your life, you might not be able to do anything to change it. Some people are ultimately closed minded. I am sorry if any of this is offensive to you in any way.