In-character insults (so long as they do not cross reasonable bounderies or server rules regarding language) are all part of the RP. Given that I interact with Kusari from the perspectives of several diffrent factions, I know how deep the animosity between factions therin can go.
However, I'm usually in contact with a lot of the players I regularly interact with in an OOC capacity, which helps a bit. While many of my characters do, with reason, spout the occasional insult at another character (with noted acceptions of Udo Ackermann and Ironwatsas) I tend to keep it well within tolerable levels. It is usually part of the character.
Example being my GC character, who has a personal vendetta with Zelot's AFA (which is his fault, btw), and the two commonly have shouting matches and frequent dogfights. In RP, she desires to, and will stop at nothing to kill and eat Ze'ev, while at the same time Ze'ev seeks to capture and abuse or kill my GC. This leads to quite a few shouting matches in character, although I can (and usually do) talk directly to Zelot afterwards on Skype, it never gets personal in an OOC capacity.
However, that has to do with their RP. Other characters have vastly diffrent RP reasons, for example Udo Ackermann, who despite being an LWB pirate, is infact the nicest, most kind hearted, and friendly person you could meet (Read: A pussy) and is really physically incapable of getting angry at anything. Insults directed at him usually only make him sad, as he is quite childish as far as his emotions are concerned.
Another example is Ironwatsas, whom insults have no effect on as he is a cold and soulless robot. He himself rarely insults others, due to his mechanistic personality. The exception being when he's trying to get into a person's head, or deliberately mess with them psychologically (in character of course).