As I understand it, the Hutu/Tutsi conflict had its roots in colonial times. the Tutsi were made the privileged class while the Hutu were relegated to the lowest rungs of society. This angst continued to fester and build until the bloodshed.
As for religion, most of Rwanda is Christian. However, as I understand it, the Hutu view and have viewed the Tutsi as Christian in name only (or, also known in American as C & E Christians, for those who only really attend services on Christmas and Easter). This led to proclamations by Hutu leaders, to include some clergy, that it was their duty, revealed by God and the Virgin Mary, to wipe out the Tutsi.
Many local religious authorities abdicated their posts or simply denied help Tutsi populations. True, some of this was out of fear of being killed themselves, yet, I believe most was out of complicity (whether religious or ethnic; most of the clergy would have come from the lower classes and would have been brought up with the same angst against the Tutsi).
It is certainly tough to completely classify as religious. However, the religious authorities certainly did not help matters by failing to condemn and failing to intervene effectively.
The Organization (HRW Report - Leave None to Tell the Story: Genocide in Rwanda, March 1999)
I would say that most of the people who are labeled as "Islamic Extremists" are not so much in it for the religious aspect as they are due to socio-economic reasons.