Welcome to OCDO!
It might help a bit if you post your location, at least the state and a general sense of where you are located.
No, they do not need to post a sign. They own the property in whichthey do business and can change the rules of entry at their will. Even though they are generally open to the public and 'accomodate' the public, carrying a firearm is not a protected class (i.e. sex, race, et al).
You might be polite enough to leave them some sort of brochure from your state (many sates have some sort of tri fold brochure on this forum) and explain your position, but then leave and take your business elsewhere. Although, I, and others generally CC when this is the case. You would be breaking no law unless they asked you to leave and you then stayed on the property violating a tresspass type law.
LIVE FREE OR DIE!