The first true religious conflict in the Middle Ages was a schism between the two main factions of the Catholic Church in the sixteenth century. This was a schism between the Dominicans (later called the Papacy) and the Dominicans (later called the Papal States) in which the former believed in an expansionist policy while the latter believed in a more conservative policy. Both sides claimed jurisdiction over the entire world, and fought a campaign of religious warfare, trying to convince the other side to join them.
This is a good source for the subject.