TRCP and IWL are not even on the radar screen in my state (Idaho), so I can't comment on them.
BCHA has a chapter here. I would not use the term green decoy to describe them. Rather, I would say they are a small "environmental" organization that has hunters and anglers as members. For example, I've never seen them chime in on things like proposed changes to hunting and fishing regs, etc., like most organization that purport to represent hunters and anglers do, so its hard to call them a hunting advocacy group (though habitat is definitely an issue important to hunting).
The only times BCHA have made the press here is when they held their convention nearby in Spokane, and when the chimed in on public lands transfer. They definitely aren't a group that wields any political influence, or has the ability to shape public perception. They seem to represent a very small segment of Idahoans. Its not clear from their website where their funding comes from, but I'm guessing its from a few large donors that aren't based in Idaho?
As I understand it, their leader for Idaho is a former Nature Conservancy activist of some sort. Ironically, here in North Idaho anyway, more land has been closed to hunting by actions of the Nature Conservancy than by any other cause, so its hard not to be a little suspicious. On the surface, it looks like the same people carrying a different flag. I'm not sure she is even actually a hunter or angler or is just part of their professional or volunteer staff? (To gain credibility with hunters here you need to show a notched tag).
Despite being a very red state, we actually have a comparatively good track record in Idaho of preserving public lands and habitat. This has been accomplished by collaborative efforts that appeal to people across the political spectrum. Some of the more radical environmental groups are very counterproductive to this process. They tend to want to litigate instead of collaborate. These are groups like Western Watersheds, GYC, Defenders of Wildlife, and the like.
Most such groups shot themselves in the feet with their unrelenting opposition to wolf delisting. They are all now completely toxic, having lost any credibility they may have had with people that share at least some common interests with regards to conservation.
My impression of BCHA is that they probably fall closer to these litigious type groups, than they do to the more mainstream groups, on the political spectrum. The fact that Rocky Barker endorses them, who is also a mouthpiece for Defenders and Wildlife and the Greater Yellowstone Coalition, does not help their cause, and creates kind of a guilty by association effect.
Most hunters I know haven't even heard of BCHA. Though, most tend to eschew these types of organizations, preferring grass roots actions, pertaining to specific issues. I would say pursuing its current strategy, BCHA will have a tough time being an effective organization in the Gem State.