All writers (including professional ones) have their characters act a certain way and sometimes it can turn real ugly, insulting, and hurtful to people. In defense they say, "well, that's the character."
But characters are not real people. They are created by the writer and they can be any way the writer wants. It is NOT something that is out of the writer's control.
So if the character is rude, sexist, or insulting, that's entirely the way the writer wants them to be. If that's what they want to do, then they should own up to it and take responsibility for the behavior. This has its place in role-playing.
However, when the negativity is directed at other PCs, then it is really no different than PvP actions and damages a game amongst strangers in the PbP environment.