I'm only forty exactly and I know who Omega is. Granted, I have the benefit of an uncle really into Doctor Who and had a working knowledge of DW trivia and lore for several years before I even started watching Doctor Who as a result, so my experience and knowledge may not necessarily reflect that of other fans my age.
I have a feeling the whole thing reporting doubters might have been a bluff. People believe doubters are rounded up, and maybe their memories have been manipulated to make them think they've witnessed doubters getting apprehended, but in fact everyone just lives in fear of doubting. After all, near the start of the episode, Belinda reported Ruby for doubting but the police never showed up to apprehend her. I suspect the real reason the Doctor and Belinda were apprehended at the end for being doubters was because the Rani needed the Doctor now for his part in her plan.What I don't get is if the plan depended on doubts, then why would doubters be reported and disappeared?