Banning a religion to enter a country is impossible, since the majority of foreign countries don't document an individuals religious affiliation. This would be comparable to the cold war where people where also falsely accused of being a communist since it wasn't actually written on a document.

In practical situations this is impossible to implement.

In constitutional terms this is an open and shut violation of that document.

In consequentialist considerations this likely will cause more harm.

On more nebulous grounds this is a departure from the identity of the United States.

If you are talking about muslims in general (not refugees but also tourists, foreigners etc.) than this would be an unconstitutional thing to do for the US in the first place and enforcing this would mean changing major definitions of the state's constitution.