My parents told me if Iove someone they will never stand in the way of that so im lucky enough I won't be in that position. They weren't thrilled when I was seeing a guy who was muslim, but more because they were worried about me because they knew it couldn't work out because of his family (it didn't work because of his family lol). If it was the other person's family I don't know if I could do it because I wouldn't want to make him choose between me or his family. I would be willing to deal with them never fully approving but I would not want to ruin his relationship with his family.
I don't know I'd have to see how much I love the girl. If I love her a lot and she makes me happy, is not religious than it would be fine. I'm ok with dating/marrying a secular girl but I would prefer she be atheist like me. If she's White my folks won't have a problem with her, but I wouldn't mind an Asian or Latino girl.
While I think it would be very difficult to marry someone whom your parents do not approve of, mainly because they have such an influence on you, that if you do go ahead it will unfortunately really hurt your relationship.
They say family, money and sex are often the reasons leading to break-ups.