If I put up a No Fireams sign or a No Trespassing sign at the entrance to the property of my residence, is that an infringement? What rights of yours am I infringing upon to ban you and/or your guns from my property?
Careful, we're not talking about bans on
people, we're talking specifically about bans on
bearing arms. What right is infringed upon with a ban on exercising
the right to bear arms?
The right to bear arms.
Why is a store owner any different? Are you responsible for the rent on the building? Are you responsible for the utility payments on the building? What exactly is your claim to a right to be present in the store and/or your right to carry a gun into that store?
You seem to be confusing the calling out of these infringements as a statement that we claim a right to be on someone's property. Not so, and you should read more carefully. We are simply calling out the infringements. Infringement = unjustified ban or restriction. A store that has an unjustified ban or restriction on the right to bear arms, by definition, is
infringing on the right to bear arms in its confines. That's not an opinion, it just is what it is. Private property owners have the superseding right, generally, to infringe on the right to bear arms with a "no guns" rule. But it is an infringement nonetheless, according to pure, objective definition.
Since you don't have a right to even be in the store, how can you claim that any of your rights are infringed upon?
Just because you don't have a right to be in the store doesn't mean you can't claim your rights are infringed upon, in the store. It's just that some infringements by the owner are permissible and some are not. For example, infringements on bearing arms and free speech by a private property owner are generally permissible. "No guns" and "No foul language" rules are infringements that are legally permissible. But they are infringements nonetheless. However, let's say you enter a store first thing in the morning, browse, find nothing you want to buy, go to exit, and find the doors locked. An employee points to a sign you didn't see: "Customers may not exit the store until making a purchase or at the end of the business day, whichever comes first". You exclaim, "Look you are infringing on my right to not be deprived of liberty except through due process of law!"
The employee retorts, "Hey, bud, I read what you wrote in a forum one time. Since you don't have a right to even be in the store, how can you claim that any of your rights are being infringed upon?"
You really can't argue against your very own words, can you?
Hope this serves to clarify the depth of error in your argument.