We also know that Islam operates on a perverse sort of case law, where the more recent decree supersedes earlier ones. Muslims and their useful idiot enablers like to quote these tolerant sounding verses, knowing full well that they were overruled by later Koranic verses and that those later ones represent the real belief system of Islam.
One of the Western tendencies that bugs me is how vulnerable "we" are to having our own cultural values turned against us. Islam is clearly incompatible with Western Civilization, and anywhere it is allowed to take root whether ostensibly peacefully or not, it will always function as a bridgehead for continued attack. We should be able to acknowledge that it is an entire political, social, economic, cultural, and religious system rolled into one, and that it is a hostile entity on all those points. Somewhere along the way we have allowed a premise to become established, and that premise is that a thing must be subject to precise definitions that accurately account for every conceivable variation, otherwise it's not really a thing. This prevents us from being able to identify threats as threats.
What I'm getting at is that sometimes prejudice and stereotyping are necessary. They are survival tactics, and we should not dismiss their use just because they fail the "precise definition that accounts for every variation" test. As a culture we used to understand that, but have become earnestly stupid since.