IMO you can't completely separate the two. Human psychological makeup (easily as complicated as rocket science) has placed traits within us to be accepted, respected, admired, liked, etc. and even to make others mad at us. You say you don't care what others think. Flip to the other side, someone is mean to you, you may do something back to them (sware, middle finger, etc.,) because you want to tick them off, because you care how they feel about you - you want them to be mad/hurt/angry at you. To be human is to care what others think of you. You may deny it or place it under another category (courtesy) but it is still lurking.
So far I have been discussing on a personal side. I don't know what you do for a living, but not caring what a strangers perception of you is would kill you in a business setting. Job interviews, new clients, customers, employees, etc. Reputation is everything in a lot of businesses. Sure you might get away with it for awhile but it would kill you in the end.