Politics and Religion

So, it's a slow night and I'm watching a movie on TCM, "The Best Man" released in 1964. It's about two presidential candidates fighting for the nomination of their party and how dirty the process can get. There's a scene early on, where the dying ex-president is talking to the candidate played by Henry Fonda and the two men are talking about the dance they have to do for the public regarding religion. Neither man is particularly religious; when asked "Do you believe in God?" the Henry Fonda character evades the question by saying he's a member of the Episcopal Church (trying to imply that he believes without coming out and saying it). Of course, he's got to play this game because it would be impossible for a non-believer to win.

The scene still has resonance today, and begs the question, why do we require our leaders to publicly demonstrate their religious faith in order to get elected? I can understand wanting to know a candidates faith, as it may shed some light on what influences a candidate's decisions, but why do so many voters see religious faith as a requirement of office? And what exactly does this requirement mean? Could a Jewish candidate be elected president? Muslim (probably not given the current climate)? Buddhist? Taoist? Agnostic? Atheist?

Just a question that I'm wondering about in this election year.