TOS's issues with religion were always kind of weird. I sometimes felt like Roddenberry was asked by the very 60s standards & practices board to not denounce modern religion (ie christianity mostly) too much since society was a lot less secular than it was by the time of TNG.
Balance of Terror had the aborted wedding ceremony conducted in what was obviously a ship's chapel (and the would-be bride also prayed/mourned in there after her intended groom was killed in the Romulan attack) and said chapel had an odd sorta-cross-shaped pulpit and a wall decoration that looked vaguely cross-like as well.
Sulu made reference to the "Great Bird of the Galaxy" as a blessing to Rand in one episode and while it could probably be a sort of secularized statement, it does also point to some amount of absorbed religious iconography after humanity gets out into the galaxy-at-wide considering Sulu is canonically Earth-born-and-raised.
There's also that running subplot in Bread & Circuses about the rebels against the it's-totally-not-the-Roman-Empire-we-swear-guys-it's-aliens ruling class who are categorized as "Sun Worshippers". Spock pointedly denounces that sun worship is a primitive superstition, and Uhura eventually corrects him by noting that they're actually worshipping "The Son of God". This revelation of Space-Roman-Jesus gets no such rebuke from Spock or anyone else, as if it's a more "acceptable" religious practice. Part of it might be the anthropological awe of the situation, as I believe Spock ponders the value of being able to watch a planet which gives them the opportunity to observe a living Roman Empire and the rise of an allegorical Christ-like messiah, but it's notable that compared to TNG pretty pointedly beating the 'superstitous nonsense' drum that TOS operating under the anti-religion Roddenberry's direct control showed a greater degree of latitude in accepting certain amounts of faith. I also recall that TNG episode with the Edo God (which was some sort of supercomputer space station or something?) being a little scornful of religion.
That said, I really don't want to have this thread turn into a theological debate or argument about the merits of quashing/exploring religion on Star Trek because that's a total minefield that is beyond the scope of this board.
In a related fun fact though: Angela Martine, the crewman who was supposed to be married in Balance of Terror turned out to be one of the very few extra/background TOS Enterprise crew members who had multiple appearances with dialogue (discounting extras and stand-in type background guys like Leslie and Hadley). She showed up again in Shore Leave (the one with the weird planet that made fantasies real, including the giant white rabbit, Kirk fighting with the guy from the academy, and a Zero strafing and killing a crew member only to have her show up alive later because it's all fake, lolz. She actually is that crew member killed by the Zero. the script apparently lists her as a different name (Mary Teller), but after casting the same actress that played Martine, her name spoken in the episode is changed to "Angela" to presumably make her the same crew member (some records credit her character as Angela Martine-Teller, which would tie together the script name somewhat with the other character, and imply that perhaps she got married to someone else in the period between Balance of Terror and Shore Leave. Though that was only 10 episodes and it was generally accepted that each TOS and TAS season encompassed about 1 year of the Enterprise's 5-year mission). The same actress was again cast as yet another different-name-in-the-script character for Space Seed, though her scenes were cut and it was never said if they would've fixed her appearance in that episode to be Angela Martine again. She also was cast again as a different character for the TOS finale, Turnabout Intruder, though this time the different name actually made it to air (here she was named Lt. Lisa and was a communications officer instead of an operations one. So unless she got married again and changed divisions, it's not the same character.)
Also, I just discovered in researching the above that as an in-joke, the male and female crew members that the bad guy in ST: Beyond kills to demonstrate his new weapon were named in the script as Martine and Tomlinson, making them the alternate universe versions of the doomed married couple from Balance of Terror. This was apparently entirely Simon Pegg's doing.
