This really isn't an issue about gender or about sexual orientation. And it is beside the point to get angy with her parents about their moral opinions--they have a right to raise their daughter according to those morals. That is what good parents do.
The worst problem here is the age issue. If both partners are over the age of 20, 3 years is no big deal. But if the partners are in their teens, then a 3 year gap is a lifetime. That's just a fact of the way that people mature.
If she is legally too young to be having a sexual relationship, it doesn't matter if it is with someone male or female. This means that you are potentially in some serious legal jeopardy that includes statutory rape, corruption of a minor, and even child abuse, depending on the laws of the state in which you live.
If her parents "play that card" they are only acting from a sense of responsibility for protecting their daughter.
Because you love her, you need to weigh the consequences carefully here. And you need to think about the future you might have with her. That means not only making responsible choices right now but also learning to create a good relationship with her parents so that they can come to respect your orientation and to approve of your relationship with their daughter.