Should I break up with my gf, would you date this kind of girl?

I wouldn't take it too personally. She's obviously still very uncomfortable with her ual orientation. If you really like her, just take it slow and be supportive. I actually have a couple of friends who have been together for years, live together, have cats they call babies together and still aren't out to one of the girls' parents. Hopefully your girlfriend won't take that long to be able to come out of the closet. But if it bothers you too much and you don't like/love her enough for it to be worth the stress then yes, you should get out of this relationship before you develop serious resentment for this girl.