How do I stop abusive customers from getting under my skin?

You can calm most people down. But the truly abusive ones leave something behind, a residue that stays long after they have gone. That is not thin skin. It is what happens when a person aims real cruelty at you and you have to stand there and absorb it. Of course it lingers. You are human, not a wall. The thing to see clearly is that their abuse was about them, not you. A person who unloads like that is carrying their own misery and looking for somewhere to put it. You happened to be standing there. It felt personal because it was aimed at you, but its source was never anything you did. You were the target, not the cause. Still, a target gets hit, and the hits add up. So build yourself a small ritual to set it down. After a bad one, take two minutes, step away, wash your hands, take a few breaths, and say to yourself that it was theirs, not yours. A small act of separation, done on purpose, keeps their poison from becoming your mood. You cannot stop them from throwing it. You can stop carrying it home.