This discussion has is not about private property but private property with public access.

In your home, you can do anything you want within the law. If you want to bar certain people, fine. If you want to block all exits in your home, fine.

Can't do that at a business. You cannot bar certain people. You cannot block fire exits. And you cannot make people speak a certain language. All you can do is ask them to leave.
But you better have a good reason.

If I enter your business carrying concealed, neither you or anyone else knows. No big deal.

If I enter your private property without permission then I get what's coming to me. But this also is a non issue. I have no reason to enter private property.

If you were my friend and invited me, you wouldn't put such restrictions on me because you would likely be carrying yourself.

And frankly, I don't care about someone's property rights when it comes to protecting myself. My welfare is worth more than someone's property. That's how it should be. And that is how it was meant to be.