Power of Beliefs

Do you think people indoctrinated into radical groups (such as neo Nazis, kkk, isis, etc) truly believe, or is their participation in the group due to other factors (loneliness, anger, mental illness, bad home, or brainwashing)?

If you ask or read about members of groups such as this, they always say they truly believe. That it is solely the doctrine that they are carrying out. There have been men to join isis who are doctors, scientists, otherwise educated and grew up in good homes. What explains their shift into radicalization? Do you think beliefs on their own are truly that powerful?