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It seems to be A Nazi by Any Other Name, but for religion, which I think is valid. It's definitely an intentional and common device used for either Our Religion Is Different (Our Gods Are Greater) or to avoid offending the audience.
However, it looks to me like it needs a Repair discussion, because the name is very annoying and the description whiny and negative, and on a spot check there are problems with the examples - two of the three Comics examples don't seem to have any relevance. (Literature and Video Games all seem to be accurate, though, so maybe they were just a too-obvious anomaly.)

Could someone explain to me what Lowest Cosmic Denominator is supposed to be about?
It says it's about works making up names for religious concepts instead of using existing ones - like "Slayer" instead of "Inquisitor", but that's about it. And I mean... that can't be ALL there is to it, right?
But this trope seems to be just too concerned with pointing out how awful and horrible and censorship-y it all is to get to the point of how and why it's actually a trope, and basically just comes across to me as "Crystal Dragon Jesus But Complaining."
Even the NAME - Lowest Cosmic Denominator as a play on Lowest Common Denominator - is just one more way for the trope to bitch about itself.