The thing is:
So the scientology gained popularity in 1980 1990 US in rich California. California is rich due to movie business. But! Our timeline and Fallout timeline are different. US in Fallout world is much more isolationistic than US nowadays. So we don't know if there was a worldwide Hollywood movie business in Fallout world. As it can be seen TV in Fallout world are like in 1950-1960 (and it is 2077 after all).
I guess world development after World War 2 was much more slower than it was in real history.
As we know California from Fallout was base for large companies like Vault-tec or West-tek, so instead of movie business apparently California went into technology development.
BTW Have a good time rewriting them
Ok, here's my rewrite idea.
The Hubologists of Fallout world could have still have developed into a semi-powerful cult. IRL scientology was founded in 1953. So, they could've been endorsed by celebrities of the pre-war, like Vera Keyes or Dean Domino (not them specifically, but similar famous people). California still could've had a movie-making business along with technological development. Maybe the Hubologists could've had ties with the pre-war US, reporting celebrities who were likely to be "communists" similar to a real life scandal during the red scare.
And after the war, I'd want the Hubologists to be hiding out underground in their secluded private bunker for years and years, until they eventually emerged to try and go out and spread their religion. When they did, they came into conflict with the CoTC refugees, Shi, and BoS, but were mostly left to their own devices in their secluded spot. In my version, they Hubologists don't want to go to space or any silly stuff like that. They just want to take control of the area, and wipe out all the heretics in order to create their own society.
Maybe they could have secretive ties with the Enclave, getting traded some cheap weapons in exchange for slaves, spies, and intelligence on the San Fran Region (not knowing the Enclave plan to wipe them out soon).
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Also, some other stuff to change.
-Make them less advanced. Maybe their secluded underground base could be full of advanced tech, but make it so that the base is all derelict and damaged, full of broken down things the Hubologists couldn't understand (half-functioning TV-screens and computer monitors) and make the Hubologists teaching less parodying of Scientology and more unique, less jokes.
-No parodies of Tom Cruise. Give them a more eerie feeling. But separate and unlike the CoTC, they aren't easily accepting of Wastelanders who want to join up; theyre suspicious.
-Maybe have them more present in the world? Have a branch in a place besides NCR and San Fran. Maybe....Broken Hills!
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Heres a question for you, Tribalus Maximus; What do you plan for the Children of the Cathedral being about in your imagination?