What I'm saying in no way contradicts that. Of course extremism of all sorts will attract those with mental issues who seek the comfort of un-nuanced absolutes. However, the fact that there is crossover on the Venn diagram doesn't mean that everyone - or even a majority - of those involved in extremist activities is mentally ill.
Much of the time the 'mental illness' thing is simply a comfort blanket that means we don't have to face up to the fact that sane men can kiss their loved ones goodbye in the morning and, with a light heart, go on to perform acts of profound barbarity the same day because their faith tells them it's OK.