Movementarianism is a spoof of multiple cults, one being Scientology, with the appearance of the Leader being based on that of L. Ron Hubbard and Movementarianism sharing Scientology's tax-exempt status in certain countries (including the US, Canada, Australia, New Zealand, and some European countries). Nancy Cartwright is a Scientologist, and had recorded a voice message for their hotline where she briefly talks in her "Bart" voice, then laughs and continues most of the message in her natural speaking voice. The producers of the Simpsons had attempted to cite copyright infringement for an unauthorized impersonation of Bart Simpson, but this was dismissed as cartoon voices cannot be copyrighted.
Another cult spoofed was the "Moonies" of Sun Myung Moon, whereby new members would enter training camps with banners and balloons that read "Welcome Home Brothers & Sisters". Training would be intensive, where sessions would last for several hours and privacy was nonexistent. Moonies were also known for "mass marriages", as shown by the Movementarians. Reverend Moon had later attempted to counter the cult image by lowering the intensity of the sessions, and ordering new members to "write a letter to your friends or family" once every ten days. Unlike the episode, Moon never claimed "mass marriages" were legally binding. Single people seeking a random hookup could not participate in the "mass marriage ceremony", as they were only for lawfully married couples seeking to renew their vows.
Yet another cult leader spoofed was Bahagwan Shree Rajneesh (also called "Osho"). Like The Leader, Osho was infamous for driving in a Rolls-Royce while his followers lined the side of the road to watch him go by, which was later featured in the 2018 Netflix documentary Wild Wild Country.
When Marge attempts to leave the compound, she is chased by the Rover guard "balloon" from the 1967 television program The Prisoner.
The song "I Love You, You Love Me" from Barney and Friends is used to brainwash babies. The Barney the Dinosaur knock-off used here is the same one from Rosebud that kept saying, "2+2 is four" before Mr. Burns interrupted all programming in Springfield. He was singing:
"We love him
He loves we
We're the leader's family"
The symbols Mr. Burns attempts to use in his religion are The K from the Kellogg's brand cereal and the Ears of Mickey Mouse from Disney.
A radio station in Sacramento uses Barney's quote after Moe uses a voodoo doll on him "Whoa, I need a drink!".
Previous Episode References
Willie, Lovejoy, and Marge are all unable to knock out Homer by hitting him with bats - this is a reference to the episode "The Homer They Fall", which reveals Homer has a protective layer around his brain which gives him a great deal of protection.
"A Star is Burns" - Homer is seen watching a movie that viewers don't actually see but just hear.
Mr. Burns' head is seen in the first row from behind as people are watching the film about "Bilsstonia", but when the camera changes in front of the people, he is not seen.
As Homer and Bart walk past the people advertising religion, the initial side-view shows two men who are gone when the camera changes angles and pans to the side: a man sitting down with a drum and another man in an orange suit jacket.
Lisa's dress briefly appears with sleeves while she, Homer, Bart and Maggie are held in Ned's rumpus room.
When Kent Brockman does a report on the Simpson family, Maggie's bow is missing on the picture of her.
How did The Leader's fake spaceship feature elaborate blinking lights if it was merely made of wood and had no visible power source seen when it fell apart?
When the "spaceship" initially powers up near the end of the episode, it emits a low-pitched hum. But after it breaks apart and reveals the Leader's pedal-powered craft, the humming (done by the Leader using a comb and wax paper) is now mid-toned.