We're talking private property, period. The concept that someone can't set the condition of not being armed to enter their private property is so absurd, I'm amazed this is even a point of contention on this forum.
The courts disagree with your contention. And if you study history, property used in business has ALWAYS been treated differently from residential property.
In you home, your rights are paramount. In other places, less so, as prescribed by law. I'm surprised you think otherwise.