In the State of Texas I have the right to carry a gun with me and can enter most places with it. I accept the responsibilities to know where it is allowed and where it is not. When my boss says no guns in the workplace I agree and abide. When the same boss tells me what I can leave out in my car there is a problem.
But you are correct. I can work elsewhere.
I'm with you. I'd have major problems with such a rule. But that doesn't mean the owner should have legal problems as a result. If we attack his property rights in order to have our way on his land, it can only come back and bite us when someone else uses the law to have their way on our land.
That's happening today, with total smoking bans in restaurants.