Apart rom getting their travel history, how are they going to vet these folks? I doubt if asking them whether they believe in sharia law, punishing gays, women, Jews, Christians, etc. will get an honest answer out of them.
They post a serious risk as a group, so should be limited to only a few exceptions - Christians and Jews and B’hais, perhaps, who are escaping a ME hellhole?
A well trained immigration officer would have no problem extracting the information. It is quite easy to trip up an applicant who is lying because they don't know exactly what you are after. Immigration officer have been doing this for years and can spot a fraud in short order.
The problem is they are NOT allowed to inquire into such matters.
The key here is that there needs to be a ideological test not a religious one.
We bared communists and national socialists from entering the US since WWII based on there ideology not their religon. So there is no constitutional problem in updating and tailoring our current admissions procedures to address our current threats.
In fact not to do so is misfeasance.