Beatlemaniacs who believed that the members of their favorite band were clean-cut nice boys like in the film A Hard Day's Night.
The term was confirmed by the Beatles themselves in a 1965 Playboy interview, where they said it was originally used by fan magazines. They picked up the term and used it to (sometimes humorously) make sure fangirls knew how perfect they were.
John: I've cheated on my wife thousands of times.
Paul: That's not true, Beatle People!
George: Yeah, I'M the one who has been cheating on John's wife.