I am a big proponent of seeking out conflict and picking fights, sounds harsh, but hear me out. It is in conflict that we have healthy dialogue and find the truth in relationships, organizations, and just generally have the opportunity to set things right. Lack of conflict is either a sign of a well tuned organization that has fought out everything there is to fight over and they are all pulling together, rare, but does happen, or, and more likely, it is a dysfunctional pit of politeness, politics and sniping.
And then there are those situations where conflict has gone nowhere. It has resolved nothing. Both camps are thoroughly entrenched and not moving from their positions. There is absolutely no point in spending any more time on these situations. If the relationship isn't toxic and the two can coexist, let them coexist. If it's toxic and slowing things down hit eject. But don't waste another breath investing in trying to make something better. Pick another battle that can have positive results and put all of your energy there.