Well, you've mentioned that if someone else came to you with this problem, the advice you'd give them would be to sever contact with this person - that may show how you really feel about what *you* should do.
I'm not about to tell you what decision you should make, but I'd suggest that you look long and hard at what the options are, and decide which one you'd regret the most, and which one you'd be glad you chose, looking at it from some point down the road. Stay with her and continue to let her say those things to you, speak up and have an honest discussion with her about how the things she says makes you feel, maintain a friendship with her but make it clear that you can't have a relationship with someone who disrespects your identity, or outright cut off all contact with her. Those are some options, I'm sure there are many other ways this could turn out, but you just have to start somewhere and think about what option feels right to you.
And this doesn't sound like it's just a "trans" issue to me. Whether she's disrespecting your gender identity or any other aspect of who you are, it's all just as hurtful. If you allow someone to treat you this way, again it doesn't matter if it's your gender they're attacking or something else about you, it's still on you to stand up for how you'll allow people to treat you. And you can't "let all trans people down" as we all have the responsibility to deal with our own issues. If you're letting yourself down, then you need to decide what you want to do about it, but don't put further pressure on yourself that you're letting anyone else down in this.
Try to take it easy and I'm sure you'll figure this out before long, it's not the end of the world, even if it may feel like it now. This too shall pass.
