I wouldn't advise anyone to get romantically involved with anyone who didn't share their own faith. It's easier to stop a fire from starting than putting one out. Romance can lead to marriage and marrying someone is an act of sharing ones deepest self and faith should be the foundation of that shared life together.
"Can two people walk together without agreeing on the direction?" Amos 3:3
"A woman is bound to her husband as long as he lives. But if her husband dies, she is free to marry anyone she wishes, but he must belong to the Lord." -1 Corinthians 7:39