We will just disagree. I view the right of self-defense has one that should be as protected as race, etc. Carry does not disrupt the store operations as nuts preaching any politics in the store, so that is a false comparison.
As far as stores not having basic health standards to meet, that is property rights gone beserk.
The argument that there are other stores is specious. Denial of patronage has a long history of controlling where folks could live and was an instrument of discrimination. Antigunners specifically argued for this privliege in the gun case in order to make carry so difficult as to be useless.
Thus, the little property rights king in his castle is not appealing to me. For such absolutism, buy an island and don't ask tax payers to provide services.