A state may consider a shopping mall to be private property even if the public is invited to enter and patronize the businesses.
Similar to my thoughts about a WalMart greeter telling customers to go F themselves. Does he have the right to say it? Yes. Can he be fired if bosses say he can’t do that but he does?
https://dailygazette.com/2010/02/19/0219_tshirt/
Court Rules Against Mall Patron Who Wore Peace T Shirt
That’s the way it should be. A private business owner should be able to exclude customers for any damn reason he wants.
Unfortunately, this was turned upside down when Federal civil rights laws were applied to “public accommodations.” Now, the security guard who removed a patron over a religious message will be subject to the same treatment under the law as a restaurant owner who tries to exclude black patrons, or a Rotary club that tries to exclude women.