It depends.
If they are incapable of accepting or exploring other viewpoints, and resort to name-calling, defamation of character based, interrupting, strawman political, browbeating and guilt tripping then no I couldn't date the girl even if they shared my own viewpoints. In other words they can believe whatever they want as long as they are diplomatic, intelligent and don't hit below the belt to win an argument.
As you can tell, I feel strongly about politics. Actually it would be more correct to say I feel very strongly about people not being able to debate politics like civilized people lol