It sounds like you are blending a Public Lands issues with a 2nd Amendment issue. BHA doesn't need to answer an AR-15 question because it isn't in their corral. Personally, I like ARs but for the size, weight, and cost they are lackluster tools for a sportsman.
If I can't hunt on public lands that is a tragedy, but I still hike, climb, bike, fish, and generally enjoy nature on those lands. Patagonia and BHA have a whole ton of common ground, and quite a few differences; we shouldn't let 2A nuances muddy that. There are other organizations that reflect those values.