Your running all kinds of sideways here.
Anyone can sue anyone else whenever the right courthouse is open, there are ramifications that will make the possibly undesirable outcome not worth the possible gain.
There is a filing fee. Without this I could sue you right now (If I knew who you are and the courthouse where you live was open.)
If you sue me, I can counter sue. It there is found to be no basis for your original lawsuit winning a false claim suit is a gimme.
When we speak of business we speak of money. If you own a business you do not want to give anyone a valid reason to sue you. Losing a lawsuit is very bad for business. When we speak of acts that violate a persons rights, we are speaking if lawsuits and civil actions (Civil/Civic? I forget which). Meaning if I am breaking no laws, all you can do is call the police and try to convince them to arrest me.
If I happen to be breaking a law, and we are talking about something actually illegal the police can indeed arrest me. By illegal I am not speaking of what Mickey Mouse scrawled on a 30 foot high neon wall. Laws.
Trespassing and Disturbing the peace are typical misdemeanor crimes that are basically there for the police to have something to arrest people for in these sorts of incidence. If the police will arrest you, which is at their discretion. If they see trouble with a 1st amendment 'conflict' they won't bother with the piddly charges OR they may hold you on disturbing the peace until that charge can be upgraded to *Whatever*.
Let me throw something out here to refocus the discussion, If I may.
You own a humongous amusement park somewhere. I get through your security and you personally see a pistol in my dufflebag when I move to store my new t-shirt. You tell someone and security arrives, when they do I sit down and do nothing but smile at you with an annoying smug look on my face.
What happens next?
Let me quickly address Tucker here as it's the same point. The Park can easily stop me from entering. If push comes to shove they will stand in my way and if I brush against them, file an assault charge. This will let the police arrest me for assault and away to the cop shop I go. See easy. By physically preventing me from entering, you don't have to deal with the 'trouble' involved in making me leave. If I try and push past you, I've assaulted you. When I assault you the fact I wanted to enter into your park becomes a moot point. This is important because since I broke a law, I am the legal system's problem and no longer yours.
I enter the 21 Club. I'm wearing shorts, flip flops and no shirt. Someone sees me juuuuust inside the door and I sit and grin. What happens?
How about juuuuust outside the door?
How about inside the door and I'm wearing a turtleneck sweater with an image of something clearly lewd and obviously intended to offend on it. I'm also wearing flip flops and shorts. What happens?
Just an idea as we may actually get somewhere if we refocus the conversation.