It doesn't sound like you're being singled out for wearing headphones, it sounds like you're being singled out because your wearing headphones caused a customer to feel ignored by a store employee. That's really not a good look for a retail store. Also, you can't be singled out for a behavior which you are the only one doing.
The customer who complained had no way of knowing that you were on break. I would assume that, had you not been wearing the headphones and were able to hear the customer you would not have muttered "I'm on my break" and otherwise totally ignored him or her. It's a misunderstanding for sure, but, had you not been wearing the headphones, it probably would not have happened and the customer would have had no complaint.
Further, you were (possibly? it's not clear from the question) not wearing the headphones in the way that you told managers that you would: had you had enough of your ears exposed that you could hear things around you, you would have heard the customer. So this incident is one in which the store has a legitimate issue.
There are a few possible solutions to this.
- Simply use earbuds as the other employees do-- there is apparently
no problem with anyone else doing it, so there shouldn't be a
problem with you doing it either. If you need the headphones
specifically then obviously this won't be suitable.
- You could speak with the manager that said there was a safety
concern (or managers, if it was a group decision, or the store
manager if you need a higher authority) and see if you can't address
their concerns even with the headphones on. This might not be
possible-- there could be a legitimate safety issue for which the
store could be liable related to your not being able to hear
coworkers. It's also possible that the managers who said wearing the
headphones was OK have themselves gotten into trouble over it.
- You could explain that you have a specific, exceptional need for the
headphones. This would probably require you to disclose your autism
if you have not already done so, and would be greatly supported by a
medical professional's note (or other statement) certifying that you
really do get a benefit out of the headphone use. But as stated in a
comment on another answer, if there is a legitimate safety concern
then this may not do much for you.
It doesn't sound like you're being singled out, it sounds like you are dealing with a privilege you enjoyed until it caused a problem (the "I was on break" defense will always fail if you were in an area where a customer can interact with you and you ignore/miss one). Now that it has caused a problem that privilege has been revoked. Your options include complying with the policy, as your coworkers currently do, trying to explore the store's actual concerns (if any) and address them, or demonstrating a legitimate, therapeutic need for the headphones. This will be a lot more persuasive than your personal statement about how much you value using headphones.
Presenting a sense of grievance, persecution, or victimization, based on what was described in the question, seems unwise to me. You, uniquely among store employees, were doing a thing, which caused a customer complaint (even though due to a misunderstanding), and customer complaints are often taken seriously in retail settings. A focus on how you can ensure that the store's goals are met in the future, while you continue to use headphones (or switch to earbuds) is how you can make sure your bosses listen to you. They'll care more about that than about what the store can do for you personally.