"Is a posted street sign - No Firearms - a legally valid sign that has to be followed.
I struggled with that part of the OP's Q, However I read it as a sign similar to a street sign in that it is shaped and colored such as many street signs are. When first reading post I took it as a sign posting a neighborhood/area.
But it seems more like a sign posted at the entrance to a building.
This is not the place to get a legal opinion, however steering someone to a place that could give them the answer is.