Saying one time that it is part of a well-known conspiracy theory may be okay, but honestly, constantly reminding me to disregard the information at every turn (and in some cases not even providing it) is, in my opinion, unacceptable if ChatGPT is meant to be just a tool. It is manipulative.
I'm certain that if you ask ChatGPT to interpret the symbolism of another movie with a different and benign underlying theory, it will even come up with some ideas on its own. However, it will refuse to do so for The Shining and the moon landing.
I've tried it with a prompt that matches my taste: "Write a short analysis in the style of a celebrated movie critique about the allusion to the moon landing that could be seen in Kubrick's movie 'The Shining'.
I got one subtle reference. I think it's safe to assume that if your prompt only mentions the moon hoax and Shining concepts with equal weight it doesn't know which one you are more interested in. So if one has some misconception in it, then it makes sense to correct you more strongly. Also, LLM-s aren't manipulating you, that requires intention which they don't have.
I'm certain that if you ask ChatGPT to interpret the symbolism of another movie with a different and benign underlying theory, it will even come up with some ideas on its own. However, it will refuse to do so for The Shining and the moon landing.