I also don't understand what you are saying about Europe. I thought people left Europe because they were persecuted for their beliefs. I don't think that someone not agreeing with my beliefs is persecution.
For example, some people believe that a candidate who believes the world was created in six days is not scientifically grounded enough to be President. Do you think such a candidate would be being persecuted for his religion?
No one is entitled to be President.
Not in public or as part of the election process. If you don't like his beliefs, don't vote for him. Don't, however, bring up his religion in the public election debate. That is not the way our system was founded.