Where do I draw the line between my religion and potential relationships? What would be morally right?

This summer I have started to hang out with this girl I really dig. She's smart, pretty and has a great personality.. However she has a different religion than I, as a Christian, and growing up in the rural south, I have been told, or "brainwashed" as many would say, by my parents that it is wrong to date someone that doesn't share religious views. My parents would profusely reject her if I brought her home. I am stuck in the dilemma that this girl is one of a kind it would be dumb of me to let her go. However, I face my parents with heartache, yes I know it is silly, but they are also paying my college tuition. I am afraid if I go on any further I could tarnish my relationship with my parents if I do date her, and I could tarnish my chance with this girl if I don't date her.

I am not afraid to do what I want, I just have mixed feelings, in that it is possible that if I date her I will basically not have the financial support or family support of my parents.

I don't know what would be worth it more, a great time with the girl which could later turn into financial regret. Or, financial support and find another girl.