This past week it has been all over the news, internet, and social media about Walmart and Kroger's attempt to control 2nd Amendment rights. However here in Virginia this has no bearing on us carrying concealed or open. First off they can put up all the stickers they want.
As far as Virginia law is concerned your open carry or concealed carry rights go out the window is Churches (church government can designate armed personnel, or blanket access ), Schools, state and federal government buildings. No where could I find any law pertaining to banning weapons in a private institution.
Many Insurance companies will tell businesses here in Virginia to put these signs up. Again it is not enforceable. I've seen them at movie theaters, bar and grills. Again not enforceable.
As far as Walmart not selling pistol ammunition I get better deals off of ammoseek.com, widener.com, outdoorlimited.com, and ammotogo.com!