A person's rights are the same whether they are on your property or not.
You mistakently think the fact that you can order someone off your property means you get to dictate their actions. Of course the fact you control the property gives you influence over them, this is not a right to violate their person.
A parking lot does not provide the same level of control as the inside of a home.
You may not allow someone to be in your lot but you have no right to invade his vehicle to determine what he has in it.
I am not arguing strict legal doctrine as we all know the government gives you very little actual control of your own property. I don't agree with that, but do agree they have an interest in keeping you from abusing your employees freedoms at your whim.
What is in my car parked in an area open to the public is just plain none of your business unless it poses some immediate danger to you.
This same principle holds for others on their property, even if we do not agree with it. Else, your proerty rights...and therefore your liberty, or worthless in the eyes of any such law founded upon their infringement (and we already have a bunch of those) and in the eyes of any such citizen who feels free to trample your rights on your property and do whatever the hell they please irrespective of your desires.
What really keeps us free is the morality that allows us to recognize other's rights and respect them. As I said, your ability to bear arms is not infringed...you can choose to boycott me and my property and remain armed, you can choose to ignore my just requests and suffer the consequences when doing so on my property.
Now...I personally would not, as a company, make such a demand. But these people are. Boycott them and their business, boycott their employ, as Squantos said. But do not use the force of law and the government to demand that they do things your way on their property. Such a premise is an awful, and dangerous two-edged sword.