Broadly (and at the risk of stating the obvious), I would say that the way to get players to stop viewing other players as The Enemy is to get them to either work or play together at something.
Tournaments were meant to work toward this goal, but I'm skeptical that they could ever have either prevented or reversed the kind of attitude we're seeing today, and from what I've seen, they've also become much less common over the years. I suspect that this is a symptom of the same thing: people don't want to throw a tournament when there's a risk that The Enemy might get the prize money, not to mention the danger of distracting your own men from the war effort.
The next obvious answer (to me, at least) is to give them all a common enemy they need to fight against. Unfortunately, given the way BT invasions have gone in the past, I don't have any confidence that this would actually get them to either work together during the invasion, or see each other more kindly afterwards.
I suppose it might be possible to create another island like the War Island, that gives a free character slot to everyone, and lump
all the players there into one big player realm, fighting against the impossibly strong forces of the Netherworld, or some other PvE scenario. However, I'm not sure how well that would work, either, even ignoring for the moment the feasibility of it from a development perspective.
I think the ideal thing would be to have some kind of big BattleMaster get-together, where everyone can actually
meet the players on the other side, and learn to see them as real people. I know small events of this nature have happened in the past, but I'm skeptical that one could be organized that's large enough to ensure that it reaches enough of the prominent players on opposite sides of these entrenched conflicts.
More ideas are welcome. And if someone wants to try to persuade me that any of these ideas I'm rejecting are more workable than I think, I'm willing to consider it, too