To Change The World Do You Have To Care What People Think Of You?

I'd like to not care what other people think of me. But I think it's an oxy-moron to not care. I mean, if I'm here to change the world don't I need to care what other people think? Like for example, if African Americans didn't care what people thought of them then they never would of fought for their rights. They would of just stayed in their all black schools and not cared. Right? I don't know! I'm kind of confussed. Do you or do you not have to care what other people think in order to change the world?