I believe in true love and I think the way you say you feel for her and about all that's happening between you two, might just be real love. And real love is worth fighting for. I'm not saying you should do something stupid like run away together, because that would only make things worse. I've been a 16-year-girl with difficult parents(and they still are very much so) so I can relate to what she must be feeling. I don't know her personally but I can imagine she feels the same way about you as I feel about my own boyfriend.
I would say, talk to her parents. Very few parents are actually simply evil and I'm not justifying their actions here but you're older than she is so you already should be mature enough to know there is two sides of the story. Try talking to them, tell them how you feel about their daughter and try to find out why they oppose the idea of you two dating, or dating as a whole. I've known religious people and they don't oppose love. Tell them you love her and you are even ready to wait for her if that's what they want. Oh, and talk to them without your girlfriend present or the discussion will most likely turn into a shouting or bitching competition. But do tell her you are going to talk to them, no need to be secretive about it.
I hope you will find a way to get through this, my best wishes to both of you!
