You have no right to make a private property owner honor your right to carry, either openly or concealed. But if the act of openly carrying is less important to you than patronizing that particular place, then conceal. It truly isn't a big deal to do so, as I assume you are doing that now. If you wish to make a political statement, then write the owner and protest, and publicize on gun forums the stores that are anti-2A.
We did not press open carry and do all this work to get it this far for you to go out and try to force it on people on their private property. We did the work so that you could open carry at your option in public without fear of arrest for that specific act. Unfortunately, you will still encounter society's scorn, at least for a while until they get used to it. But consider, why in open carry states, is it relatively rare to see an open carrier? Perhaps it's because open carriers, despite having the right, are considerate of societal perceptions and only open carry when it's "acceptable" to do so?
I'm just throwing this out there, to each their own!