I think it will be hard to avoid the cops getting involved in most western countries unless the fight is over pretty quick. In other countries things can be more "fluid".
I've seen, and heard from others, police either look the other way or simply watch ready to step in if things begin getting out of hand or weapons appear. The type of authority also matters. In America a town sheriff will probably view it different from a state police trooper since he likely knows the people involved.
For example, in the Philippines they have the national police but they also have the barangay security (neighborhood quasi-police). They live in, and usually grew up in, the neighborhood and almost certainly know the fighters, all of the bystanders watching and probably the reason for the fight. Most times I think they assess the chances of immediate serious injury, take a moment to evaluate the situation and bystanders then slowly move in and separate the combatants. Unlike in America though they usually just send everyone on their separate ways once they calm down.
