Well, in the grand scheme of things, no.
I mean, I might a little when it comes to how it will affect me. Nobody really would just be apathetic if they couldn't get a job they want because of employer's opinions or whatever. So, when it comes to things like that, yeah, everybody really needs to be somewhat conscious of how they come off to others.
BUT, when it's a situation or another person whose opinions really don't effect you in anyway... then no, I really don't care. I used to. I used to hide my inner self from others because of fear of being rejected and stuff (I used to have to deal with others teasing me, calling me names, picking on me, and just being straight up mean. They would love to attack the fact I loved games and REALLY attacked the fact I played Pokemon like nobody's business. - HECK, I STILL play Pokemon like nobody's business. xD), but as I've gotten older, I've realized that almost EVERYBODY, is an idiot. And, they really don't effect me. In fact, I think I sometimes like to do things JUST to annoy the haters. Like, if I like something that most others seem to dislike, or talk-$hit about, I will start liking it harder, showing it more that I like it, and I even might actually like it all that much more.
Now, I do though have to say that, the only time now, that I care about what others think, is when they might be misunderstanding me in some way. What I mean is, I want them to know what I mean when I say something, and that they know just what I'm all about. er- if that makes any sense... I guess what I mean is, I don't want to mis-represent myself. (in a basic way) That's why I refuse to wear anything that isn't my style. Because it's not me. I want to be myself, and show myself, the way I want myself to be seen. AS ME. I like things that are on the darker side. So, I wear a darker style of clothing. I will NOT be seen in anything pink, simply because it is not me, and it does not represent who I really am inside. I dislike the color pink. Quite a lot, actually.
But anywhoo... all in all, I really don't care what people think about me. And I've learned that public opinion really doesn't matter. Though, nothing really "matters" but that's another topic. I could get into it, but that's best left saved for a philosophical discussion.