OK.
So imagine that this group is 100% successful in carrying out their mission in the US. Armed with their success, they take their show on the road to the rest of the world, starting with the Muslim countries and are 100% succesful again. They then take a quick swing through Asia, Africa, Australia, Antartica and Europe leaving a world only populated by Gays and Lesbians.
Then what?
Oops! Strategic error! Law of unintended consequences in action.