The problem with a "Good" secret society, is that by the very nature of good and evil, evil can infiltrate the good organization with impunity - while a good person doing the rites of evil as a spy, will become tainted in at least some small way and/or be found out easily.

Good cannot and does not need to hide, I feel any organization like this should do it with fancy logos and "neighbourhood watch" signs and stickers on shop windows, it should have the moral authority in the public space, with it's eye ever watchful, while evil remains in the shadows.