The primary difference between the situation you describe and this situation right here is that those licensed casinos actually DID promote gambling and drinking. They wouldn't even have denied it; it was their stated business. This rejection now is almost certainly on grounds of what is essentially NOT true - that D&D is satanic or what have you. The fact that they believe such to be true is not really a valid defense; we who play such games know it to not be, and have a right to let them know our displeasure. Change only comes through enough people making their voices known.
The only plan I see here is to simply withdraw support and funnel it to other charities. I realize that's hard to do for anyone not financially capable of supporting in the first place, but the fact is, all the angry emails in the world are unlikely to produce results other than catharsis for the writer. Well, it might get whoever made this decision fired, but that's probably about it. The money has already been donated elsewhere, so the horse has left the barn.
The important point is that we, as gamers, don't allow this sort of smear against us to interfere with our plans to help the needy in the future. We just do it through another organization.