It’s a free country. This sort of boycott would just result in Black Rifle Pizza.
The moral of the story as I see it is: not acting because you don't want a backlash is a loosing game - they'll find a reason to backlash anyway.
(I don’t have this at my fingertips, I just happen to be driving through Montana and my wife asked me about the Black Rifle Coffee billboards so I literally just read the Wikipedia article a couple of hours ago.)
The thing is that both of these are cynical pledges. I’m not like yay starbucks on this - i’m sure they were doing it for the PR and because refugees are easily exploited workers. It’s one of the things I hate about reactionary backlashes - by creating “sides”, i find myself on a side with people i don’t want to be on a side with because the other side is dumber