Players shouldn’t take in-character events so personally. I think, however, that this can’t be avoided, especially when it’s player-versus-player. If a random GM NPC gets the better of a player character then the player generally accepts that as failure against an element of the game (unless of course, the GM is playing a Mary/Gary Sue GMPC, but that’s a different matter entirely). But if another player gets the better of them then things can get pretty colourful.
I was running a Star Wars game many moons ago in which a player created a character working against the other players, an Imperial spy feeding information back to his superiors. He had to make rolls to make sure he sent this information out without being discovered but I did not tell him if he failed or not. In fact, I was rolling secretly for the other players and once they beat his roll I let them know, secretly, what he was up to. It was up to them to decide whether to confront him or feed him false information. In short order they set him up, confronted him and then, after a failed escape attempt on his part, they dealt with him. One dead traitor PC and two very satisfied PCs.
The player in question wasn’t happy about being found out and killed so quickly – even though it was him that wanted to create a PC to work against the players and make himself an enemy – and it made it even worse in the fact that he had been found out and stopped not by an NPC but the other players. He quickly created a new character. In the very next game, the first chance he got, he dropped the other players into trouble and tried to kill them. For no reason. At all. There was nothing about the character that would justify such an action, and he put all his dice into combat skills to make him incredibly tough to beat. He simply created a combat-heavy PC so that he could kill the other PCs for stopping his previous character from doing his nefarious deeds.
I can understand players being upset with other players if they obstruct, kill, loot and otherwise annoy their PC simply to be annoying. God knows I’ve seen enough of that at the gaming table. But some people take it too far, take it very personally even if the events and actions in the game are justified based on decisions and actions, and they let it colour their perception of the game for a long time. In fact, the games with this player broke down very quickly after his assassination attempt because no matter what characters they played or what game they played in they simply couldn’t trust him not to make an attempt on their lives at some point. Their in-game decisions weren’t based on the characters they were playing but on what kind of mood this particular player was in. That’s not a game, that’s a joke.
Keeping the feelings of the player separate from the player character is a definite in my book. You can get emotionally involved with the PC, that’s for sure, but when the game is over then the game is over, and harbouring resentment against other players isn’t the way to go. If the player is being a total dick and is simply out to get you then that’s a justified complaint but it should still be dealt with outside the game. ‘Hey, mate, I’m not really enjoying that and it’s kind of ruining the game for me. Can you not?’ It’s as simple as that. But getting revenge for some imagined slight by plotting and scheming and trying to kill a PC that another player may have spent months investing their time in, and in turn derailing the game to pursue personal vendettas – that’s not great.
Just remember, in the absence of any evidence to the contrary it’s not personal, it’s roleplaying. And if you set yourself up as the bad guy, working against the rest of the group, don’t be surprised if they stick a targeting signal transmitter in your backpack and then bomb you from orbit.