When Whoopie Goldberg and Bill O'Reilly are our cultural standard-bearers; when the POTUS takes pandering to its apotheosis in positively Orwellian revision; when, to paraphrase Eric Voegelin, pneumopathological delusion trumps reality and realism (he means both metaphysical and the political) is insanity, then what hope is there for civilization?
Thankfully, WG and BO'R are not our cultural standard-bearers, and King Barack must stand for re-election.
Still, the problem you raise is, as you say, a "mighty" one. You will recall this entry of mine, in which I treat of Mosques and Men?
I object to the use of terms like "Islamist" and "Muslim extremist" on the grounds that they are ill-informed, chauvinistic, and (in the case of "extremist") dangerously misapplied (dangerous, that is - does it not go without saying? - to language). Words have no meaning if reading the Qur'an and taking what it has to say seriously makes one an extremist.
The Islamist is one who would see the absolute rule of Shari'a, and the disintegration of infidel political modes and orders. This is what Qur'an calls for explicitly. Anyone, who submits to its dictates as God's perfect revelation, which is to say, any Muslim, is bound to work toward precisely such ends. So, Islamist is a critically useless neologism.
Ave crux, spes unica!