We have nearby National Conservation Areas, managed by the BLM, also. They are NOT under the National Park Service or National Wildlife Refuge system, and therefore did not benefit from the law that allows carrying there.
I do not know if there are centralized BLM rules for National Conservation Areas, but our local Red Rock National Conservation Area in Nevada allows unloaded carrying of firearms. The BLM doodz are actually quite polite about enforcing it, but still send people to their cars to comply.
However, a National Recreation Area is under the National Park Service, and does qualify. Lake Mead National Recreation Area between NV and AZ is an example. Some of the signs came down after the law passed, but many did not. They do know the law, though, and don't say a word to you, even in the areas that still have the signs up. It apparently isn't anyone's job to remove the signs.