I was caught in between a two-person (whose names cannot be revealed to protect their privacy) yesterday.
When two people have differing views (and vehemently sticking to them) and get into each other's path, it is inevitable that sparks will fly.
And it usually takes a third party to help (or forced to help) resolve it.
How the conflict is resolved by the third party will gauge the person's competency in dealing with relationships and can be a good gauge of the potential of his management skills.
I told my wife how I tried (emphasis on tried) to resolve this conflict and she was "relatively impressed" given the constraints that I had in dealing with it.