lots of ways around that.   Our immigration rules and required documents for travel are NOT all the same for every country, not do all countries has the same expectations of American travelors of immigrants.    International law is rife with identifying risk of traveling in many countries.

I see no reason why we can't have specific processes based on country of origin, or even a combined profile of various factors.    I think it is dissingenuous to say the only factor is religious affiliation for those who want tighter screening.    (at least for rational people, no doubt some are solely focused on religion)