The only place I've ever shot on BLM land is Nevada. Even at the "popular" spots I used to shoot at near Vegas, there were rarely other shooters there, much less other recreational users. At the same time most of these areas were pretty trashed from years of activity, shooter and otherwise. My last trip through the area a favorite spot of mine was closed due to a pipeline being built through it, and the portions away from the pipeline were marked as "wilderness restoration areas"(paraphrasing but something to that effect) It was nice to see the desert shrubbery taking back the areas and no signs of public dumping.
That being said it would be sad if they cannot reach some sort of compromise rather than singling out recreational shooters.
It seems it would be easy enough to post signs/modify the current ones that areas are open to shooting hopefully reducing the concerns of people getting worried by the sound of gunfire. Temporary closures of frequently used areas until they're cleaned up by the individual users and local shooting groups, makes much more sense than outright restrictions. From what I've seen in the places I've lived there always seems to be a group or two willing to shoulder the burden of organizing clean ups at public areas, my feeling is that these numbers would increase if there were more regular temporary closures due to littering, which from what I've seen is a primary concern. This would also hopefully increase the number of individual users who actually give a darn, and clean up after themselves.