Example: Finding a common goal to work towards with opponents
One excellent example of how opposing groups can work together comes from a famous study in social psychology by Muzafer Sherif and his colleagues. At a summer camp, two groups of boys were intense competitors for trophies and prizes. Their opposition became so strong that the "Eagles" burned the "Rattlers'" flag; the Rattlers retaliated by vandalizing the Eagles' cabin. Matters might have gotten out of hand, except that the camp truck broke down on a trip; both groups had to join forces to get it started. The common goal ("superordinate goal" was the technical term used) helped restore harmony between the two groups.
The moral of the story is to look for things you have in common with your opponents, rather than on the differences you have.