In a round about way, you have nailed the issue. We should not be allowing people from cultures antithetical to ours to immigrate here, especially those groups who have proven themselves to be unwilling to assimilate. We are inviting problems and social discord. That is what really upsets me. Issues like this are completely avoidable.
Once someone is here, they have equal protection. You could make a case that based on empirical evidence we are importing future murderers. How do you deal with a presumed future murderer under our constitution?
Not going to do a lot of research, but Lucky Luciano was one, and he had decisively aided our victory in WWII.