Yes, but mostly in terms of how I conduct myself. If someone thinks I'm strange, I couldn't care less, but if they think I'm R. Rudey Rudemeister then I have to become all apologetic and try to show myself to be a decent guy.
Which is why I'm polite to people I don't know, shop for clothes often, be nice to people, try to leave a best impression, and fuss over my hair. I know it makes me sound like... a total shallow girly-girl, but really? It sounds worse than it is. I'm NOT a total shallow girly-girl. It's the truth for me and a bunch of other people, as I believe. Deal with it. :0
I think its interesting how many people claim to not care when Im pretty sure no one likes a nasty comment, from a stranger or not, no one likes to be insulted in public or online, very rarely is anyone completely unaffected by insults, rudeness, verbal abuse, internet attacks, even by complete strangers, online or not.
If six people at the bus stop next to you say 'Oh my God I've never seen anyone so damn ugly in my life' to you I dont believe anyone would completely not care even a little bit. You'd go home and cry, you'd tell your friends, you'd maybe respond and bite back, get angry, get depressed, you'd think "wtf??!" - but completely unemotionally not care on any level like some kind of robot ... nah.
As someone said, "if I didn't care, I would just go outside with my pyjamas on and bedhead" - best comment in the whole thread. Many people like to maintain an air of not caring, hell, "I dont care" has to be the most (over)used phrase of the last decade. I doubt many really mean it though, you would have to be very unemotional and have skin made of concrete.