I think fanatic extremists are not necessarily mentally ill. They might have self esteem problems, feel like outcasts in society at large, and benefit from some therapy, but I don’t think they are all mentally ill.
People who are mentally, obviously are not all fanatic extremists.
There is crossover some times.
If someone is raised thinking their religion is right, and that God wants them to do extreme things, and they believe what they are told, because that’s all they really know, are they fanatics? Or, just a product of their environment?