Between the various ST shows, only once was a specific Earth religion assigned to a character. Harry Kim on Voyager was a Catholic, but it was not mentioned much, especially after the first season. The same thing was used in Falling Skies with Lourdes Delgado, also a Catholic. Of course, she gets mad at God and that’s the end of what might’ve been an interesting challenge for the writers.
In the original Star Trek series, there was an episode, “Bread and Circuses”, that did not address a denomination but a belief in the Son (which the landing party thought the natives worshiped the sun). The final dialogue was a nod to the Messiah repeating His earthly visit on another planet. There was a Ray Bradbury short story, “The Man”, they probably stole that idea from.
“It is a simple thing, it is the word of Vaal.”