We all live our faith. We just don’t make a huge deal out of verbally inserting it in secular affairs. Especially when it comes down to dealing with secular nations. This is something Islamic countries do.
Rudy is a Catholic who supports abortion and has been divorced twice. Is that living his faith?
Mitt is a proud Mormon, but he was for abortion before he was against it: Members of The Church of Jesus Christ of Latter-day Saints must not submit to, perform, encourage, pay for, or arrange for an abortion. Church members who encourage an abortion in any way may be subject to Church discipline. Does Mitt live his faith?
Clearly not every candidate lives their faith. Try finding one on the Democrat side. I picked out these two because their failings are glaring, not because they are unique. There is nothing unAmerican in living your faith openly as a presidential candidate, regardless of what that faith might be. It is also okay not to vote for someone because you disagree with him. Where you are wrong is in equating the personal religion of the President as somehow being promoting a state religion. That's what the muslims do.