I would strongly petition my employer to remove the requirement that I wear it. If he refused I would amicably resign and move on. It's his business. His reputation, His money funding it. He should have the right to set the rules no matter how screwball or ridiculous.I don't struggle with it at all.
I've got no problem with companies requiring employees to wear uniforms, but these are symbols that have been added on the uniforms that have nothing to do with the company itself.
What would you say if a company decided to add swastika symbols to a company uniform?
Also if the emphasis of the business was in that direction, I would quit anyway. But I would not think it ethical that I sue him over a policy I didn't like.