Considering that Islam is both a political and religious system, in which community laws (sharia) are the direct word of g*d, it is trickier to make a decision that would be "politically correct"...
and what about Muslims fleeing Islamic tyrannies? I recognize that not all Muslims are 100% religiously faithful.
It is a hard question. But I think I would err on the side of caution when it comes to America's safety
Let' suppose you have 3 people; A, B, and C.
A is a known terrorist, B & C are not.
If A communicates with B; I think we should be able to spy on that communication because A is a terrorist. But if B then communicates with C, we should not be able to spy on that communication.
...unless the communication between A and B establishes that B is a terrorist as well.