Business owners in my state do not have the legal authority to forbid customers from carrying concealed firearms. Employment is an agreement between two parties and is completely different subject.
I would argue that laws precluding such signs are also un-Constitutional.
You might be right but that doesn't change reality one bit.
We've already established that a property owner can bar people from exercising Constitutionally protected activities on their private property (you kicked the satan worshipping Obama campaigners off your lawn).
No we haven't. The rights privileges and immunities guaranteed by the constitution to the individual can't be nullified simply because one is on private property. An individual can be asked to leave a private property but their rights cannot be violated. As an example, if I had satan worshiping, Obama campaigners on my lawn (but I repeat myself), I could ask them to leave, but I couldn't legally gag them or use an oxy/acetylene torch to melt their pentacles to their chests.
Just as you don't have the legal authority to forbid people from worshipping Satan...But a property owner can assert whether or not they're going to accept that practice on their property, and if they ask you to leave and you don't, you're trespassing. You're being pedantic, but in spite of your parsing, it still amounts to a de facto authority of a property owner to assert the right to allow or disallow armed persons on their property.
"No we haven't. The rights privileges and immunities guaranteed by the constitution to the individual can't be nullified simply because one is on private property."
You conveniently overlook the fact that the property owner's rights are among the rights, privileges and immunities guaranteed by the Constitution. Just as you're under no obligation to allow persons to exercise their protected rights on your front lawn, no property owner is obligated to allow you to exercise your rights on their property.
"Can I carry my loaded and concealed firearm (assuming I have a license to do so) in a New Hampshire business (public place) such as Costco that has a NO FIREARMS sign posted? NO, private property rights prevail. If you are caught carrying a firearm in a business that is properly posted prohibiting firearms (i.e. the sign was of a sufficient size-there is no law precisely defining the ―prescribed manner of posting‖ i.e. what size and type the sign must be-however some guidance may be found in New Hampshire R.S.A. 635:4 Prescribed manner of Posting 40) and posted at the entrance where you entered (thus you had notice) you may be asked to leave (only someone with ―authority‖ can ask you to leave, typically a store manager or even an employee of the store may be deemed to have ―authority‖) and you could be prosecuted under New Hampshire R.S.A. 635:2. 41 See State v. Gaffney, 147 N.H. 550 (2002). (When defendant refused to leave the police station after being asked to do so, there was sufficient evidence to convict defendant of criminal trespass under former R.S.A. 635:2, II (b) (now R.S.A. 635:2 III(b) because defendant received strong warnings to leave the station or risk being arrested.) You can be asked to leave even IF you do not have a firearm and even if you believe you are not doing anything wrong, as a business, even Wal-Mart is private property and has a right to control who is allowed on the premises (assuming they are not violating federal law, by, for example posting a ―NO X race allowed‖ or keeping a federally protected category of individuals from entering).