Here's Rodney Ascher's 2012 docuмentary film "Room 237" about Stanley Kubrick's telling of the moon landings story in the film "The Shining."
I've been watching this and it's compelling. If it isn't a matter of Kubrick leaving all sorts of references to Apollo 11 then there are lots of coincidences. Not being skilled with numerology and symbol-finding, I don't know that lots of other messages, totally unrelated to NASA and Apollo, couldn't be found in the film if one were to look hard. It's possible to count the cars in the Overlook parking lot in such a way that they make up the date of the first step on the moon 7-21-69. But couldn't you rearrange 43 cars to represent anything? D.B Caulfield is a stretch, as representing Kubrick selling out. If anything his claimed involvement with NASA boosts his profile and makes him seem a genius. His movies are overrated.
The eagle statues in the office, the Indian totems do look like rockets. Adler is German for eagle. Danny with the Apollo sweater. Room 217 in the book changed to 237. Interesting stuff.
In the beginning of the movie Kubrick's meeting with Mueller and Slayton is mentioned. If his meeting with them was for ulterior motives I don't see why it would have been publicized, with photos taken, unless they needed a cover story. Kubrick hired Marshall Space Flight Center personnel Fred Orway and Harry Lange, and they relocated to England to help with pre-production.
This source says that the purpose of all this was to ensure the scientific accuracy of his 2001 project.
I'd think NASA would employ a team of special-effects people, but I don't see any use for employing Kubrick. I don't even think Kubrick is a very good storyteller, so the claim that he was hired to write the scripts for Apollo 11, 12, and 13 sounds fishy. Better to hire some very skilled screenwriter who has a vested interest in the conspiracy.
The Oleg Olleynik article referenced is above my head. For those interested the
people here claim that it's bunk.