I spent the better part of the first year of my carry looking for posted signs in CO. Did not find a single one, so I don't even look anymore (READ - I don't even read any of the signage on the doors or windows, unless the door is locked, then I look for the hours of operation).
The only "No Firearms" signs that I have ever seen have been at the airport security checkpoint, and the main Post Office distribution hub (local stations are not posted - let's not go down that road).
In the event that I may actually encounter one, I may or may not respect the wishes of the business owner, it all depends on why I am there and how bad I need what is inside.
If your state is not binding with the signs, then I'd say it is personal choice to respect it or not.
However, if you go a traveling to another state, it is a REAL GOOD IDEA to spend several hours pouring over their carry laws before you go, especially if that state allows individual cities to set their own laws regarding CC (Nebraska for example).