Sure, there have been problems with other than Muslim groups. The Irish "troubles" come to mind. The Basque separatists.
But to pretend that radical Muslims are not a problem now requires that we ignore reality. Israeli airport security works. Rational minds would think we might copy some of their approaches, and get over our squeamishness about "profiling." There is no room for political correctness when lives are at stake.
And, by the way, nothing we do would require that we violate the U.S. Constitution, either. That's a red herring. Political correctness is running amok, and standing in the way of properly protecting people. It's absurd that the FBI didn't stay on this case after being alerted by a foreign intel service.