Harry Hay was a Communist, and he told his fellow "gays" that Communism would "liberate" them when he knew exactly how Communist regimes actually treat them.
In his days the only place they could hide was the Communist Party. Today they can realize their goals through various Protestant communities, or liberal party associations, etc.
They also infiltrate conservative organizations as a fifth column, be it the Catholic Church or Evangelical communities, or conservative party circles. Even if they can't expect to succeed in some of them, they can climb up the corporate ladder and then create scandals when they come out. It's done for effect.