I use the credit union branch in Dayton...but rarely go inside. I had noticed a long time ago they had a no gun policy. Despite that...I've stayed with them as my bank. They've treated me extremely well as a customer, something I can't say about the other banks. It is a bit of an uncomfortable trade off.
No legal weight, same as any other private property. It just states their wishes. How we respect that is up to us.