Honestly I'm not sure there's much you can do, from what you've said I get the idea that this person ties hating a minority into their identity, it's not a matter of ignorance or just being edgy it's something that informs who they are and in that kind of situation all the evidence in the world won't change their mind. You're probably a feminist so have you ever tried convincing an incel that women are people? It's a similar thing. I'd say the best you can do is make your opposition to her beliefs known and don't let her say shitty things unchallenged. Maybe someone with more experience might have some ideas but even convincing my family who're just kinda ignorant of trans issues felt almost insurmountable and only worked for me because their young (4-5) grandkids started correcting them on my name and pronouns and eventually they started having an am I the bad guy realization.