You do know there are many gun owners that advocate for passing laws that make signs stating a property is "gun free" to be unenforceable as a matter of law right?
And view "gun free" government buildings to be unconstitutional
For my part I see the signs as useful. If I see a "gun free" sign on a business that just tells me to spend my money elsewhere if possible.
Even when the shoe is on the other foot, e.g. a baker who does not want to disseminate interracial or same-sex wedding cake?
Deferring to "that is a crime" is no help because your argument is that it should not be a crime to refuse to disseminate speech you don't like.
There is no principled way to draw a line here. Either you don't compel speech or you do.
There are many, many gun owners who argue exactly that. That "gun free zones" are anti-Constitutional, be those zones publicly owned, or privately owned.
This shouldn't be news to you.
It's directly analogous to my previous example. It is illegal for businesses to deny service on the basis of skin color. It isn't, however, illegal for a private residence to do so.
Refusing to rebroadcast or support the opinions of someone you don't like is at present not a crime, and I sincerely hope it stays that way. Because otherwise you have to apply the same logic to other rights. And that sort of extremism leads to some crazy outcomes.
For example, in the US the 2nd amendment is, under the law, of equal importance as the 1st. So should I, as a gun owner, demand that I should be allowed to carry my firearm anywhere, on anyone's property; and claim that for them to deny me that right is a violation of my 2nd amendment rights? I'm pro-gun and even to me that sounds crazy, as it would to many pro-gunners who are usually big on personal property rights. There's a reason Full30.com exists.
Or how about the right to freedom of assembly (also part of the first amendment)? Should I be forced to allow protesters to use my property, as disallowing them violates their first amendment rights?