What if the Great Schism between the Catholic and Orthodox churches in 1054 was averted and never happened? This means that the Pope has all power over the eastern churches and for at matter in the ERE, How would this effect relations between the ERE and the western european HRE? How would this effect politics and diplomacy at the time? How would this effect, say the crusades or other wars. What about science? Butterflies are huge.
I know many will say disagreements between churches will be inevitable and all, but lets say this original schism never happens, so maybe the Pope could become more powerful, so other independent Christian denominations could eventually arise, but they'll probably be minor and few and far between.