I'm sorry to hear about your frustrations.
I think most feminists have someone in their life like your friend. In an odd way these people keep us in check -- they challenge us to be more clear about our ideas and our feminism, at least that's how it seems to play out.
At some point you have learn to "not take the bait" as my friend always says -- you need to just assume that you two don't/won't see things the same way and fighting about them won't bring you closer on these topics. I understand your frustration, but you have to let her figure these things out on her owm -- at this point, she might be doing it just to get you angry. As for how she can have those thoughts -- I think in part it's just immaturity, if she doesn't believe women should have the right to vote, I hope she exercises that by not voting.
People are often ignoring their own situation and often have these opinions because they don't want to feel singled out. I hope that helps -- instead of trying to explain, just show her through your own example how you are living a feminist life and how you are all the better for it.