Religious doctrinal disagreements can be settled neither by reason nor by evidence. Therefore, either an attempt is made to enforce uniformity or disparate denominations coexist indefinitely. We should see more Christian denominations in Poul Anderson's History of Technic Civilization and I think that it is unlikely that the Anglican Church would rejoin the Roman Church after SM Stirling's Change. If I were Anglican, then I would not accept reunion on that basis but my belief and practice lie elsewhere in any case.
1+1=3, i.e., if two churches or political parties merge, then some on both sides join the new organization whereas others on both sides refuse. Result: not one but three. Ninian Smart suggested that, when two traditions meet, 1+1=7! See here.