The answer to your question depends on the state you’re in.
As someone else (essentially) said: signs on Colorado do not carry the force of law - you have to be asked to leave, and refuse, before you can be charged. Same situation in Kentucky.
In Ohio, though, if you knowingly enter a conspicuously posted place, you don’t have to be asked to leave in order to be charged.
In Arizona, you COULD be charged with a misdemeanor-level criminal trespass. You probably wouldn’t be arrested if you agreed to leave, but the owner has the option. The sign is considered your notification to leave (or not enter).