Property rights are not absolute as discussed many times. Businesses have to follow health laws and cannot discriminate against protected classes.
Signage on businesses used to include:
No Jews, Blacks, Irish, Dogs, Indians, Asians, etc.
That is not permitted and that is righteous.
Gun rights have not reached the level of protected classes.
However, application of your rights has to be weighed against clearly defined safety issues.
One might argue that if you wanted carry to be protected it must be in a safe manner. It is clearly the case that the OC Long Arm crowd in many instances carry in a very UNSAFE manner.
Concealed carry doesn't generate those safety concerns.
You would have to pass legislation to aid carry as a protected issue to trump property rights. I would go along with that for concealed carry unless there is a technical issue not to carry. You might disagree. However, I wouldn't argue the Long Arm OC is the manner we have seen is safe and should be be protected, such that property rights are voided.