I used to work retail and the best way I had to deal with things like this was not taking it personally. Granted, it is extremely difficult to do. I had trouble with this as well. I would take comments personally and I almost cried in front of a customer one time. That didn't go well. Anyway, just know you're not alone in having this experience with people. Also know that sometimes there's nothing to be done about the situation, and all you can do is apologize (if you feel like it), and just offer to get whatever it is done that they want. Is there a manager you can talk to about this? Also, maybe try focusing on the positive interactions you've had with customers (if there are any) and just put your mind on that (I know, it's easier said than done). Some people I know adopt kind of a "brusque" attitude with customers - I'm not sure I would recommend this, as it seems like this doesn't necessarily help when they get mad. I'll say for people like me (a sensitive person), it's really hard to interact in this way with people, given that I take most things personally if they're insulting. Or I'll think about the person's motives, or whatever. It's really hard.

Addition: I would also try to think about lowering the bar. I guess what I mean by that is - what are the expectations for the interaction (this is something I still struggle with to this day). The expectations are that the person working completes the transaction successfully. That's about it. I mean, sure there can be small talk or whatever. But just maybe something else to consider if you're having trouble with this.