In my opinion people should be able to keep characters roleplays seperate, have a clear roleplay for each character and stick by it. That way you could be in two opposing factions. The problem is people might find ways to use their other character for their own good.
Another issue is, how can you stop them even if it wasn't allowed.
People should kill their enemies, if there are two sets of enemies shooting each other, then help one kill the other, then kill the ones left.