I reject the idea that people shouldn't care what others think about them. We are made to be social creatures. Without honor and shame society wouldn't function.

Ironically, those who say you shouldn't care about people's opinion of you often resort to name-calling, demonstrating that social esteem is inescapable.

And this is a good thing. Communication is given to us so that we can have an effect on the world around us. The serenity prayer does not mean we ought to give up and isolate ourselves, quite the opposite.

The solution to being hurt isn't to withdraw into stoicism, but to realize that God has offered a seat of honor at his table to you, an undeserving sinner. 

"For do I now persuade men, or God? Or do I seek to please men? For if I still pleased men, I would not be a bondservant of Christ."

This is the only escape from the tyrrany of others' opinion - not to give up caring, but to know whose opinion actually matters.