I have seen factions done. I have seen it done in an… okay manner. It was baked into the theme. But there were always players who took things too hard, and went too hard, and made it less fun for those around them.
I do think that it’s possible to do CvC (but not PvP) antagonism, so long as it’s managed very carefully.
As others on this thread have pointed out, I think it starts with transparency, includes making outcomes not involve character death, and then I think that it moves on to making it clear that the conflict is Characters vs Character, and that the players are all there to work together to make a fun story. Even then, all it takes is one sore loser or sore winner and things can spiral out of hand.
As far as transparency is concerned, I think that it’s important for players to know what they’re getting into, how the conflict will be adjudicated, and what the possible outcomes will be. The example that @Aria gave is a great one – up until the one Staffer changed things up.
When character death is on the line, players get twitchy. I think that if you can make sure that death isn’t on the line, people are more likely to engage in CvC conflict in good faith. Starting a new character from scratch when you liked the deceased one, or they had some cool gear/stats, or they had great connections – it can be incredibly frustrating, and people will act in bad faith to avoid that frustration.
I do also think that one thing that can help is making sure that the opposing factions are fighting past each other, not fighting against each other. As an example, way back on KotOR MUSH, we had the Sith and the Republic fighting over a neutral system. Except they couldn’t attack each other, because if they did, then the neutral system would support whichever side was attacked. So each side had to work to make the other side look bad, and themselves look good, without ever actually fighting one another.
It’s been long enough that I don’t honestly remember how it turned out – it may have collapsed into complete crap – but I like the general idea of it as an opportunity for CvC antagonism. It means that no PC is directly beating up another PC, so there’s no chance of death (or even maiming).