The Constitution lays out the frame work for the federal government, and limits its powers to those listed in it. The Bill of Rights is there to protect us from the FEDERAL government. Up until the 14th Amendment was passed, the states had NO restraint from the federal government on violating the Bill of Rights. Even today, not all of the Bill of Rights have been incorporated to the states, which means, that the state government can still violate them without repercussions.
Private property rights generally trump Constitutional or other rights. That is why forums, such as this can ban people who use language, or post topics that the administrators don't agree with. It doesn't violate the 1st Amendment. HOWEVER if it was a government run forum, then a 1st Amendment violation could be made.
Another example is dress codes, while not specifically listed anywhere as a right, I have the "right" to wear shorts, sleeveless shirts, or pretty much whatever I want as long as my "private parts" aren't exposed. However a business can set certain dress standards if they wish. I went to a Dave & Busters where one person with me wasn't allowed in because they had a sleeveless shirt on. Their "right" trumps mine.
A "no guns" sign is in all reality similar to a "No shoes, No shirt, No Service" sign. Nothing in law says I have to wear shoes, but as the owner of private property, the owner has the right to ask me to leave if I walk in without shoes.
Do I wish every business allowed firearms? Of course, and I think we should work on getting those that do prohibit them to lift that restriction. However, I think it would be a big overstep of government to dictate what a private property owner allows, or disallows. Much like the smoking ban, I don't like the smell of cigarette smoke, but I HATE that the government forced private businesses to go smoke free.