Do you think it's bad to talk shit about a customer in my store?
Do you think it is rude to talk like that about a customer?
Yes, but he started it by asking for some discounts.
You shouldn't be saying such things especially to a customer while you're at work. You may end up losing your job because of it regardless of how justified it is.
I don't care about getting fired for saying what I think.
You should care about your job and you should respect the customers you get. You need to make a living and need to have a job so it is better to be polite until you can find something else.