Hell beyond sexual violence in conflicts, H. sapiens has a long cross cultural tradition of using marriage to seal peace. Sex to resolve conflict is also present in one of our closest extant relatives (the bonobo), though not in their closest relative. We know very little about Neanderthals' behavior. We don't even know to what extent their behavior was cultural vs instinctive. If prior to reestablishment of contact sapiens were sending daughters as part of peace (as we did until relatively recently) while Neanderthals were sending sons and nobody wanted to fight over this difference you could wind up with an entirely cultural reason for this split.

Topics like these greatly sadden me as I think of all the cousins we killed before we even had the technology to write about them. What a fascinating world it must have been to have other members of our genus around, and how sad none were in any of the places we reached last.