Not caring what others think of you isn't the same as actively trying to screw others over or just being rude if that's what you're alluding at (I'm guessing). For example, "not caring what others think" and just cutting in-front of a queue is an objectively dick move. So in that sense, yes it's self fulfilling (but this is not what "not caring what others think" means).
Perhaps a good example of a positive "not caring what others think" might be dancing however you want; you don't feel embarrassed because you're not a good dancer you just do whatever.
Perhaps another good example is Bob is a vegan and hates that you aren't; now you don't really care anymore and can focus on eating the food you want to. Flip the roles, Bob eats whatever he wants and hates that you're a vegan; you again don't care.
Actions are different from thoughts. We're judged/arrested when we do that. What people think, on the other hand, is immaterial to whether one should be happy or not.
If one is required to be concerned with not "being an asshole", how are risky ventures ever undertaken?
It might be dangerous, but it is useful to feel righteously self-justified when about to do something that will lead people to logically deduce that you're an asshole !
