How to Robot: Stop taking it personally, but don't turn off your emotions. People are people, and if they insult you, you do not have to take it. You do have to pick your battles, tho, and that's where you can improve. The more you know where those lines are, the less you have to concentrate on paying attention to them, the better you'll become.
It's harder for some people (me, for example) than others.
Don't go out of your way for these people. Go out of your way for the people who make you feel good. Otherwise, hit your buttons and move on knowing that the next person won't be like that.
Edit for something interesting that came to mind: When I call Apple tech support, they do not parrot my issue. 'I'm sorry that you're having problems with <exactly what I said>, Mr. <my last name>.' No, you little shit, you are not sorry and I want you to stop acting like a robot. Apple's response is much more human, like, 'Oh, let's try to fix your <underlying issue> then.' Incidentally, this is the attitude of most upper tiers of tech support, if you end up with them. I don't think this is coincidence.
I guess what I'm saying is that you 'robot' by not acting like a drone.