Philosophical debate aside, when it comes to the value of a friendship, what's important is mutual respect. It's one thing when we see and experience the world in a way that our friends don't understand (and vice versa), it is something else all together when our "friends" think it's their right (or duty) to force their beliefs down our throats.
I have had friends who really did not understand or agree with my transition. Especially in the early years of my transition, I invited one or 2 people that I respect and trust to make every effort to talk me out of it. I figured if they could talk me out of transition, then I had no business transitioning. Those friends did not hold back their opinions about why they thought I was making a mistake. And we had some very lively debates on the subject. But our discussions were always in the spirit of friendship first, mutual respect at all times, and love. There was always give and take in these debates, and we would actively listen to each other and try to understand where each other were coming from. I never felt judged or preached to.
Where there is judgement and inflexibility, there can be no friendship. If that's what is going on with this person, then it's time to cut her loose. At least, that's what I would do.