Is it rude to ignore someone, maybe someone you don't even know, for no reason?

This question was prompted by another question, asking if it was rude for customers to be talking on their cell phones as the cashier is trying to check them out. Some feel it wasn’t rude, I do. I said it was the same thing as ignoring someone, which is always rude, unless you’re angry with them and that’s the best course of action to take. In this example, say the customer isn’t talking on their cell phone—would you consider it rude for that person to just ignore the cashier, as if they didn’t exist?