Let's just put aside the fact that religious discrimination of this sort cuts directly against America's supposed founding values (I mean, cuts directly against the same Founding Fathers toward whom your patriotism boner is always supposed to point). Islam is not a country or an ethnicity--it's a fucking world religion that a quarter of the world's population subscribes to. Here's a handy list of Muslim populations by country: https://en.wikipedia.org/wiki/Islam_by_country . Where's your proposed cutoff list for banning immigration from a country? Does Malaysia not make the fucking list? I'm sure you'll herp derp in response about how the answer is obvious (you know, one of those Mooslem countries! We all know!). But it's not fucking simple at all. What if some Kurds who are technically from Iraq (98.9%) get sick of fighting and want to try the American dream?
You want a religious affiliation test at the borders? Check for circumcised dicks (as long as they don't, uhh, look Jewish)?
The practical problems with your non-solution hints at the conceptual basis behind your non-solution and why you're so worked up about it. Islam is one of those global/international phenomena that keeps thwarting your patriotic/nationalist/nation-based worldview. (Yes, terrorism is another one.) You keep looking for a conveniently locatable national enemy for the U.S. to be opposed to. The actual world doesn't work that way.