Personally for me, the way I try to approach this is that if I'm RPing a particularly divisive character I'll outright tell people from the start that I'm sorry for how they might behave, and that I hope the two of us as real people can at least be friendly even if my character is being utterly ruthless. In fact if I'm playing a particularly unpleasant character I'll often lay down what they're capable of, so that the other person knows what they might be getting into and can reject it accordingly. Likewise, if I'm playing a fairly decent character but they do something that might put others off, I open a discussion with the other roleplayers first and let them know what is about to happen. If the subject matter is anything more than a simple argument, I'll usually also ask for permission as well. Most people don't really see the need to give permission, but I feel it opens the pathway towards mutual respect and understanding when you put another person's comfort first. I've found most fights and misunderstandings tend to resolve themselves, or even avoid happening in the first place, with even just the most basic amount of communication.
