It depends, really. As Citrinin said:
"I care what my friends and family think of me, yes. And there are certain situations where I care what strangers think of me, like a prospective employer in a job interview. But, aside from that, no, not really. :/"
I do care what people close to me think. But, when it comes to strangers (other than employers/job interviews/etc), I really don't.
If they don't like me, so be it. They can just learn to accept people how they are.
But, if something's blatantly obvious like my shoe is untiedmy hair's out-of-whack or something like that, then I don't mind them pointing it out/whatever they do.
Like I said, it just depends.