Signs do not carry the weight of law. Say you went shirtless into a store that was posted "No Shirt, No Shoes. No Service". Would you breaking the law or a rule? The answer is a rule and they would ask you to leave. Now if you refuse to leave this is where you get in trouble. Refusing could result in a trespass charge.
The answer is rule and you would be asked to leave. The same applies with No Guns signs.