The way you handle a rude customer says more about you than about them.

Someone being unpleasant tells you about their day and almost nothing else. What happens next is yours: the tone you pick, whether you stay level, whether you get smaller or louder. People watching learn more from your half of it than from theirs, because theirs is random and yours is a choice.

On your next shift, pick one line you will use when someone is difficult and use it every time. Having it ready means you are not composing under pressure. Afterwards, let it belong to them, not to you.