As per the title, sometime after the rise of Islam - say post 800 AD, make it so that the majority of adherents of Islam and Christianity adopt this philosophy. Islam and Christianity manage to move past their pasts, and see themselves as part of a single religious group, no further apart than Catholics and Coptics.
Bonus Points if
- The positions of Caliph and Vicegerent of God, both exist.
- These positions are held by the same person.
and because I'm a complete Byzantophile
- Have the leader of this united faith be of Roman/Byzantine descent.