There are two issues here: the legal issue, and the moral issue.
The legal issue is fairly easy. Some states allow property owners to restrict carry, and some of those states attach criminal penalties for disobeying such limitations. That is where these laws become unfair, IMO. (Trespassing is different) Think about it- a movie theater can ask you not to speak during the movie, but you will not go to jail for doing so.
The second issue is the moral one- and this is where the debate here rages. Some believe that a property owner should have absolute authority over others while they are on his property, others believe that there are limits on both the property owner AND the entrant, and still others believe that the RKBA is absolute. I believe that both of the absolutist positions are incorrect.
If you open your property to the public, you voluntarily assume certain responsibilities over the people that you invite onto your property. That is the basis for fire codes, emergency exits, and the like.
As far as I am concerned, the laws of my state do not require me to obey your wishes in regards to my right to defend myself and my family. I will not abrogate that responsibility, unless the property owner has taken steps to secure my defense in my stead. Simply demanding that I disarm, while making no provision for my safety, and refusing to take fiscal responsibility if a criminal attacks me while I follow your policy allows a property owner to assert authority without accountability or responsibility. Demanding that I disarm and hold myself defenseless while refusing to provide for my security is disrespectful of my rights, and I refuse to honor the rights of someone who would so callously leave me to die.
I refuse to disarm so someone can save a few bucks on his liability insurance, unless the law requires it, or unless he has taken steps to insure my safety that go beyond merely posting a sign. When I can, I will take my business elsewhere, but when I cannot, I will continue to carry.