Any law which deprives a business of the right to control access to their private property, and the terms thereof, is a blatant violation of property rights. We cannot, and should not, defend gun rights at the expense of something so fundamental.
I'm not arguing for gun rights in this instance, but indeed property rights. My automobile is my property. The State has an interest in knowing what's in my car only so long as it is moving on a public road. They can require that my car bear identifying marks for several reasons, including the possible recovery of my property if it is stolen, as well as the enforcement of requirements to insure it for operation on public roads. The State can search it under (too) many circumstances, usually in connection with it moving on a public road.
I disagree that my property rights in my vehicle, and my rights in the other property my vehicle may contain, are conditioned by where that vehicle may be, whether moving or parked.
If I keep a piece in my car, and the car and the piece are lawfully mine, it's nobody's business whether I have a piece in it.