If I were the business owner, I'd tell them to shove the sign up their ass. Sideways. In no uncertain terms. Whether I supported the union or not, no one would tell me what kind of signs I have to have in my store or who I have to publicly support. If it meant I had to lose a few dollars, so be it.
But that's just how I roll. It's that whole "freedom' and "rugged individualist" thing I just can't shake. Some pencil-necked asshole telling me I have to jump aboard their train or face the consequences, well, just makes me bristle. I think it would most Americans, too.