Well, when I've found myself in situations like this, my first thought is to use my position as an (technically) outsider to try to help. Now sometimes this can't work and backfires, but it's also one of the biggest benefits of holding that role. So it comes with some obligation to use it.
Sometimes an 'outsider' can really see the trees for the forest as they say, and end up shedding much needed light on something. Something you can't see from 'inside' because you are simply too close to the problem.
Now, this does nothing for your own 'needs' so it does require a cup of selflessness. But by nature of how these things work, if it happens you can contribute something to their situation that solves something, the gratitude will likely generate something coming back your way in return.
And in the possible case that what's brewing below the surface that's stirring conflict indeed has something to do with some perceived conflict of your role, it helps underline the positive role you play. And the more you become an asset and less a threat, the faster the relationship grows.