I am not familiar with the latest Illinois mess of laws to skirt the SCOTUS rulings. It sounds like recent state law has bestowed legal ramifications beyond trespassing upon persons otherwise legal at the whim of private business owners.
For those that do not know, in most states (that I am aware of), there is no legal authority or action beyond trespassing that can be taken against a legal citizen who does not recognize or conform to a posted “no guns” sign on an establishment that has not been designated specifically by law (ie. schools, government buildings, etc.).
In other words, a business can ask you to leave the premises if you are carrying (concealed or otherwise). If you refuse, they can call the police on you for trespassing. It seems Illinois is now radically different.
IL law patterns KS law on a state-specified sign being a legal notice that can result in charges beyond simple trespass. So IL is not the only place. My home state of OK follows your description on simple trespass for failing to leave when told.
As to the overall ISRA material, my problem remains with the treatment of firearms as an onerous civil right that can be restricted at a whim. Years ago, many restaurants posted signage about “reserving the right to refuse service to anyone” and that’s been trumped by the various civil rights acts since 1965.