Back to the planet earth.
Your hypothetical has zero to do with this case, obviously your intention.
Try ‘ Have em’ put up a sign that says queers can't no-one can hold hands, kiss, and/or snuggle in the mall and see how that fares.’
Now that's the same. You have zero right to do that on others property too.
If you don't like it then don't do business at the mall, better yet rally others to not do business there too. That you have a right to do.
There is no such thing as, "no one" or "everyone" when it comes to restricting a behavior. Behaviors have been upheld as a form of free speech protected under the First Amendment and furthermore, some behaviors are classified as political speech that cannot be restricted when a member of a protected class engages in them but not when someone not a member of a protected class engages in them.
"Your" property is far less "yours" than you think it is if it's open to the public.
Regards.