From Hit and Run:
Moscow Girls Make Me Sing and Shout: As we plow through all those Sgt. Pepper's retrospectives, let us not forget the pioneering work of Gary Allen of the John Birch Society, who in 1969 exposed the Beatles' links to world communism. ("That Music: There's More To It Than Meets The Ear," American Opinion, February 1969.)... Allen had a surprisingly simple approach: Take "Back in the U.S.S.R." literally, and assume everything else has a hidden meaning.
Thus, "Magical Mystery Tour" is about drugs ("Roll up, roll up [your sleeve] for the mystery tour," he decodes), as is "Hey Jude" (cf. "let her under your skin"). And "Revolution"'s slap at Chairman Mao is:
simply telling the Maoists that Fabian gradualism is working, and that the Maoists might blow it all by getting the public excited before things are ready for 'Revolution.'...In short, 'Revolution' takes the Moscow line against Trotskyites and the Progressive Labor Party, based on Lenin's Leftwing Extremism: An Infantile Disorder."
Which isn't to say the Beatles themselves were necessarily responsible for those messages. Allen... believes "the reason the Beatles and other folk-rock groups received such success in the music field was because they were backed by the Entertainment Section of the Communist Party." He also quotes trumpeter Joseph Crow, "possibly the country's Number One expert on musical subversion":
Neither Lennon nor McCartney...had technical training in music. For them to have written some of their songs is like someone who has not had physics or math inventing the A-bomb. It's possible, but not very probable. Because of its technical excellence it is possible that this music is put together by behavioral scientists in some "think tank." I know from personal experience that it takes a great deal of time to create complicated music and lyrics, and I don't know when The Beatles would have time to put this kind of stuff together. They are always on tour, vacationing, or making a movie...