Is it rude to ask people about their ethnicity?

At work today, I had just given a customer her order when she asked me, “What’s your background?”

I don’t mind talking about my heritage, but I was caught off guard a little because I’ve never been asked that sort of question by a stranger before. I know people become curious because of the way I look, but isn’t ethnicity a little bit too personal a subject to discuss with a stranger?