Private businesses that post a no gun sign, whether that sign has the force of statute is irrelevant in my opinion. The property owner's requirements for entry are made known prior to my entry onto his property. I will respect his requirements and go elsewhere. Those who enter his private business while armed knowing that the owner prohibits armed citizens from entering his property are not interested in private property rights as an absolute right.
A private non-business property that posts a sign must be respected regardless of statutory mandates, or the lack thereof.
Your call to make for you of course.
Personally I'll not claim to know what your interested in or not.
Where I live the sign means less than nothing, no law broken by ignoring one, because there is an absolute right to be armed and the property owner has no authority to interfere with that.
There isn't even any case law to support them even applying to OC here.
That said I will ignore no gun/weapon signs without a 2nd thought.
On the other hand I have no right to be or remain on said privately owned property once told to leave for any reason as the property owner does have authority about WHO is on their property. If asked I will immediately leave.
Though I've never been asked too cc or OC