If they were born with both and chose one, I wouldn't have a problem with it. If they switched genders, then the whole a man should not become a women thing would really bother me. I'm a gay friendly Christian, but that would be my breaking point regarding a serious relationship. I wouldn't mind being friends though, and would treat them like anyone else as a friend.
That being said, I'm not available and doubt this would ever come up.
"And everyone's Kickstarter has merit." - Malory Archer