Well I wouldn't say it is right to change because no one likes you. I mean it depends if that part of the person tends to hurt the people around them. It might be that the person makes a lot of mean jokes and people get hurt. In the case their intention is not to hurt anyone then they should alter their behavior. This is because the intent is not achieved through the action.
In reality though I don't think people are not set in stone. I think people change in time and change in circumstances. I mean that I think people are more fluid than one might think. It is a path of self discovery... I am still trying to figure out who I am. I might think something is part of my identity now then years from now think in the opposing manner.
I was mean when I was young and people respected me and I was actually fought over... I became nicer even though I find people take me more for granted than they did when I was mean. I am not willing to change. I am happier now because the friends I have suit me more. I am with those who respect me even if I do not enforce respect.
In my opinion there is also a little room for change. I mean small things can change without changing the core of the person. It just needs to have a personalized limits. These limits can change over time.
It is up to the individual to respect their own beliefs to the extent that pleases them the most. I mean life is short so just do what brings the most inner peace.
I hope this makes sense...
Bottom Line
Identity is fluid.
Respect yourself.
Behavior can change to reach the intent.