Overhearing "ABBA Boy" in a record shop - What should I do?

I'm sorry about that situation you're in.

I don't know other people's culture very well, but in America, I heard that backfiring someone could lead to a lot of trouble (and it did, in most cases!). I'd advise not to start a record riot. You never know when you do something and you become a laughingstock for most people.

Every situation is different from someone else. One size doesn't fit all.
If my record store cashier calls me "ABBA boy" or "krautboy/jazz-cat", then I'd take it as a joke. 

But, in your case:

If it gets worse, then go ahead and confront them. I'm not writing "be mean to them" or "be nice to them", just convince them not to call you ABBA boy in the most civil and dominating way. Otherwise, try to make yourself the best of being assertive. But know your limits; don't go threatening them with self-harm or inflicting assault toward another.

If you're happy with what you're doing, then keep doing it!
If you're buying, let's say, The Beach Boys or Carpenters, then that's you that's making the choice doing so, not someone else. Why should a tease negatively influence and change you? You don't want to be a puppet to someone else. You shouldn't abide by someone who'll put you down. Rather, make light of the teasing and then be nonchalant and insouciant about that libel that someone talked behind your back.

If you feel uncomfortable with the record shop, try going there on a different day than what you usually do.
I don't know if you should go there anymore, because that would be the last thing I'd want to do, in my opinion; if all things don't work, there goes the last resort.