Banning all known Muslims from countries that have active terrorism in them support it etc is very doable. It has been done in the past with ideologies, nationalities, race, etc. The US Constitution has no jurisdiction in other countries so a ban can be by religion.
Which is my point, to a degree.
Easier to temporarily ban people coming in from Syria, than temporarily banning only muslims coming in from Syria.
You can figure out they came from Syria easier than you can figure out if they are muslim or not.
If you can figure out both, fine, works for me, but it is easier to lie about your religion than it is to lie about what part of the world you came from.
Although, I suppose, you could lie about both.
So neither solution is 100% foolproof.
I'd go with ban from the region, followed by the religion.
Seems more logical to me.