It's the poorest of manners to ask me in only to throw me out. To use or threaten force in the affront is simply intolerable.
Last I checked, manners were not spelled out bylegal statute. Please cite your source.
Shirt and shoeshave long since been accepted as "rules" for these establishments. They politely ask that you do not enter unless in compliance...in spite of their "invitation". You certainly have a right to go barefoot wouldn't you say? There's no laws that say you MUST wear shoes. But, a business has the right to require them and no one would argue that.
Asking, or "inviting" customers' to enter without weapons is no different. Yes, they've invited you, but, under their terms. No one would argue that simply because they "invited" you, that you could just help yourself to their possesions and walk out. As a GUEST of their property, you must act in accordance to the property owner's guidelines.
Just because I invite you into my home does not mean that I still cannot tell you to leave your muddy shoes outside. I still have the right to tell you to conduct yourself according to the rules of my home. You would not, for instance, be allowed to put your feet on my furnature, and it would be considered just plain rude of you and I would be well with in my right to tell you to leave and if you do not comply, I'd then be well within my rights to call the cops and have you forcibly removed.