The Catholic Church? All this nasty material stuff isn't the real you, there's a magical kingdom "beyond" all this where you could live forever in your sparkly immaterial form, Satan has dominion over this world, always seeking ways to deceive you. It's all a big mystery you can't understand. Don't believe your mind, don't believe your senses, just believe and obey us cough cough, I mean God.

For secular antirealism, I recall Hitchens relating that the reaction to Orwell behind the Iron Curtain with respect to DoubleThink was "how does he know?" I don't believe that the communists had an official antirealist stance, however. They were supposed to be scientific socialists. But when it becomes illegal and dangerous to disagree, people are forced into making statements contradicting their own minds, which is antirealism in practice if not in "official ideology".

And of course, saying "I am antirealist" is not the kind of direct factual statement one should expect out of an antirealist. I'd expect mysterion or collectivist piffle.