However, there is a Constitutional right for the private ownership of property. Under current law, a publicly traded company still retains all rights of ownership just as if a citizen owned the property in question. Be it land, buildings, vehicles, or patents.
If the State can take from a company the free exercise of the rights of ownership of property, and forcing a company or a private citizen to give up their property rights if favor of someone else’s rights .... say their right to speech is not acceptable to me.
Consider this scenario. A person, without your permission, walks onto your property (away from the public sidewalk or public access entrance), say into your lawn and puts up a Hilary Clinton for President sign.
Yes that person has the right to free speech but they do not have the right to use your property to exercise their free speech.
There can exist no "private property" belonging to a corporation without corporate law allowing the creation of such corporations. I don't think it unreasonable to limit such "private property" such that employees and perhaps other law-abiding visitors cannot be disarmed.
There are plenty of limitations already on such "private property". Just try to design a parking lot for such "private property" without including parking spaces reserved for the disabled.