Going by its long history; the beginning of religion and its assertions through time lied in disagreement with opponent religions. If within different religions people ever lived peaceful life at any time, it was because of compromise, they avoided open expression of disagreement and conflict giving preference to harmony than misery.
Modern Christians factions now uniting is based on above guidelines. Their maturity has shown them the futility of their religious divide, or even religious unite. If so, there have been some natural learnings in them that peace and harmony is not a function of religious unite, but the handmaid of one’s own self.
Your emotionally suggested line - how beautiful would that be to find all the Muslims united in the bond of universal brotherhood and sisterhood is simply puerile, if dreamed within the ambit of religion or tribal Arabian powers.
Shouldn’t we grow in a better way than that?