I think the not caring comes from realising that generally, it doesn't matter what most other people think of me.
I don't think there's many people who don't care about ANYONE elses opinions. They just only care what the people important to them think.
So for instance, I love DP and DD and want them to remain in my life, so I care what they think of me. I want DP to remain in love with me, so I treat her well and show her love and affection.
I cared what my Mum thought of me, but not my Dad, because I think my Dad's a knobhead so I'm not really bothered that he finds me boring.
I care what my boss thinks of me enough to keep me employed, but I'm not really bothered that he thinks I'm a bit of a stubborn git. (Mainly because I keep my work/life balance and won't work a weekend just to fit his unreasonable timescales)
I care enough about what my friends think of me that I try to make sure that I'm good conversation and fun when I see them. But I don't care that they think I'm a crap cook, because me not being able to make them a decent meal isn't going to kill our friendship.
Mostly though, I try to be a good and decent person because I care about what I think of me, not anyone else. I don't screw other people over because I'd have to live with myself afterwards, not because someone else if a dickhead.
Things get cared about on the basis of whether they're going to affect my life. The fact that Sheila in work hates my dress sense has absolutely no bearing on my life. DP loathes my music taste. She's not going to leave me over it. Steve on the school run took an instant dislike to me years ago because I bailed on a playdate last minute (DD threw up). Again, not going to affect my life in any way.
None of those things are going to affect my life negatively in any way, so they don't get cared about.