The mission of the NRA is to protect our ability to acquire, possess, collect, exhibit, transport, carry, transfer ownership of, and enjoy the right to use arms. There mission does not include protecting public lands from transfer, nor should it be. Each organization has to pick and choose what fights they want to participate in, resources are not infinite for any organization. My membership supports my ability to own firearms.
BHA fights for hunting and fishing on public lands. Although you could infer that supporting hunting means supporting firearms their focus according to their mission is for public land access to recreate. My membership supports them to do just that. I want them to spend the bulk of their resources on public land issues, and not get involved in 2nd amendment protectionism.
RMEF mission is to "conserving, restoring and enhancing natural habitats; promoting the sound management of wild elk, which may be hunted or otherwise enjoyed; restoring elk to their native ranges; and educating members and the public about habitat conservation and our hunting heritage." Again, no mention of firearm protection even though hunting elk is part of their mission. My membership is to aid in the conservation efforts for Elk.
Each 501c focuses on one specific purpose. Say the NRA decides that PLT is just as important as the 2nd amendment. They would immediately alienate members who think PLT is a good idea. Their membership would dwindle. It just doesn't make sense.