That said™, I'd be very surprised to learn very many concealed carriers ignore those signs: we're not only law-abiding, but uncommonly polite. I have to admit I've never seen one one of those nasty signs, living as I do near Colorado Springs. Denver and Boulder want to be, respectively, the San Francisco and Berkeley of the Rocky Mountains; the rest of Colorado remains solidly American. I've been told local movie theaters put up criminal appeasement signs, but haven't gone to the movies in at least fifteen years: too much mindless violence masquerading as "entertainment" and one-gag movies trying to pass themselves off as "comedy."
2923.126 Duties of licensed individual.
3) (a) Except as provided in division (C)(3)(b) of this section, the owner or person in control of private land or premises, and a private person or entity leasing land or premises owned by the state, the United States, or a political subdivision of the state or the United States, may post a sign in a conspicuous location on that land or on those premises prohibiting persons from carrying firearms or concealed firearms on or onto that land or those premises. Except as otherwise provided in this division, a person who knowingly violates a posted prohibition of that nature is guilty of criminal trespass in violation of division (A)(4) of section 2911.21 of the Revised Code and is guilty of a misdemeanor of the fourth degree.
A fourth degree misdemeanor can get you 30 days in jail in Ohio and cost you over $2,000. Aside from that, 99.9% of CCW permit holders are EXTREMELY law abiding and would not ignore the sign even if they could get away with it for the simple fact that it would be illegal.