“No, but they have the right to ask you if you’ve been vaccinated before you enter their property. You don’t have to answer or get vaccinated, but they have the right to ask you not to enter if you refuse.”
You sure about that? Is it only for the Covid vax, or can they keep out anyone for not having any vax? Ebola? HPV? If only for Covid vax, why only that one, legally?
They can keep anyone out for pretty much any reason that occurs to them unless it’s based on sex, race, age, religion or disability.
Most of them would be stupid business decisions but they don’t give up their property rights by inviting someone in to shop.