Killing in a roleplay game is a complicated thing, seeing as killing in real life is a TOTALLY different story. Killing in a game confers none of the consequences or the mental burden that killing in real life would.
The character that I play 9 out of 10 times is a sociopath of sorts with deviant criminal tendencies who was born in blood, and has little remorse for his actions. Despite this, I can't go around simply killing people for the hell of it because my character is a psycho as this would be against the rules, and not to mention, bland. So I try to play him inspired by the main character from Dexter, if you are familiar with it. Leon must find ways to satiate his tendencies, all the while fitting in with society, avoiding getting caught - to 'survive.'
So with that being said, for the most part my kills tend to be with regard to rivalries between criminal groups. As you may know many in criminal groups tend to kill one another for petty reasons. I try to avoid this and encourage more well thought out reasoning behind going after a rival. If you are a rival and you hassled one of my brothers, you can bet your ass that I/he would feel no regret in cutting you to pieces, or simply sending you to the afterlife with a .50 to the brain. I and the character are above killing for petty insults. If the murder in question is for more questionable reasons, I try to take it up with an admin or the victim to make sure there are no qualms in the end. After all, it's all supposed to be for fun, right?
To sum it up, I tend to pay no mind petty insults that tend to have reasonings based outside of roleplay. Wronging someone I give a shit or getting in my way about is an entirely different story.