The link below pertains to those of us in Oregon, but I would imagine other states have similar Statutes in place.
In Missouri the state laws do limit some places like police stations, hospitals, and courthouses. Some other places such as schools and churches are given latitude to grant or restrict according to their board of directors. All other places are legal to carry, however property owners/businesses may ask you to leave if they choose.
They can post no gun signs but they have no force of law and you can ignore them. If you do, however, and they catch you they can ask you to leave. If you do not, they can call the police to remove you and you can be charged with trespassing. That is not a firearms related violation, though.
Sounds like Oregon is doing something similar.
Yep. Sounds very familiar.