You would have to vet no one if you just shut down immigration entirely and most freepers would be fine with that. We don't need to continue flooding the country with more dependent democratic voters.
And what about people who say they are coming as tourists, students, on business, and the like? How do you prevent Muslims from sneaking through that way? Or would you cut off all foreign entry into the U.S. period as the only way to prevent Muslims from entering?