Through enlightenment we have come where we are today.
Enlightenment taught us the values of free speech, free elections, reason over faith,... It just didn't show us how to defend ourselves against people abusing these tools with the ultimate goal of disbanding them (s the Nazi's did with democraty for example). Somewhere we should come up with a system which is tolerant of tolerance, but tolerant of intolerance... But that's an argument no-one has ever been willing to look into, and which has sadly has the tendency in becoming just plain intolerance.
You raise a couple of valid points.
That being said, I do not believe that every refugee who arrives here is a threat to our own system, and I do not believe that they come here with a conscious intent of subverting our culture.