In so far as you want to fit into society, or a certain part of society, you're going to care about the opinion of that society or part of society. It can't be helped. The problem becomes disruptive for some individuals who become obsessed with what other people think. "Oh, he didn't smile right away. He doesn't like the dress." "She frowned at me; what did I do wrong?"
My favorite saying on this topic is, "Don't worry about what people think about you. You'd be surprised how seldom people DO think about you."
No honestly for me... i don't think caring about other people think about you is going to matter. you're you there them. Why should you care about what someone else thinks about you? There thoughts aren't gonna affect you nor are your thoughts gonna affect there lives in any way.
Of course you should care. It is through respectful, regular interactions with other people that we grow and change and learn more about the world. Other people's impressions of us help us develop into the kind of adults we can live with. The tough part is deciding whose opinion ranks above others.
To a point, yes. There are certain rules that every culture has, and if you deviate from those rules, there will be consequences such as shunning, gossip, and even violence. Luckily, we live in a time when you can be pretty much whoever you want to be! Yes, be individualistic and pursue your dreams and goals :)