I am asking if a property owner can do this, can he also prohibit who carry HIV from coming on his premises?
Firearms that are carried concealed on the person are only being carried for personal protection. They are not being carried for any public display or use. Indeed, in my own state the law states that a concealed weapon must remain concealed in public except when necessary for immediate use.
Just as HIV is a personal, and private, matter, so is the issue of self defense. Nobody can provide self defense for me. What I carry in my pants is my own business. That is where I would draw the line with respect to the property owner’s right to draw conditions of entry to his premises.
If laws explicitly stated that business owners were not responsible for the actions of concealed-carry holders with their weapons unless they carried weapons as part of their duties, and if laws also explicitly stated that people who post "gun free zones" are liable for any harm that comes to people therein, how many businesses would post "gun free zones", even if they were allowed to do so?