Network push religion? No. Push back against blasphemy? Yes. So, for example, in TOS "Who Mourns for Adonais" the network did not approve of Kirk's line "Mankind has no need for gods" to end there, but required or requested it to be softened and not blasphemous. So, "We find the one quite adequate" was added.
Yet, the entire point of late 2nd season's
"Bread and Circuses"--from Septimus and Flavius speaking of their belief (and in contrast to the false god-worshiping Romans) to the episode's coda with Uhura's revelation about
the Son, that episode appeared to have been created with a very pointed message in mind. Episode writers Coon and Roddenberry did not
need to adapt / write such a story at all (from Kneubuhl's original story), nor were they forced to by NBC. Further, if Gene
"He was always a hardcore atheist!!!" Roddenberry had issues with a story that openly acknowledges Jesus's identity and His impact, one of his many changes to the script while it was shot probably would have removed or watered down the unambiguous name / legacy drop. Roddenberry could think on his feet, so he could have substituted Jesus with anyone (i.e., create a character for his fictional Roman planet), but the script, final cut and aired episode remained unchanged.
During this time there was nothing on television that was blatantly anti-christian.
Well, that depended on the perception of the audience member, of course; ABC's
Bewitched (1964-72) and
Dark Shadows (1966-71) were both accused by some conservative groups of not only promoting every dark, supernatural idea under the sun, but
not professing (through characters) any real world religious beliefs (
Shadows had the Trask family, but they were portrayed as fire & brimstone-styled zealots). Even so, the
ABC brass did not agree, or accuse
Bewitched's EP/co-creator Bill Asher or
Dark Shadows' Dan Curtis of being anti-Christian, and did not attempt to add or promote real world faith and religion on their respective series.
Likewise, belly buttons could not be shown on TV
...about that...
That was another bit of G.R.'s blarney, albeit slightly tongue-in-cheek. In fact, NBC lifted the navel ban starting with Trek's second season. We saw women's belly buttons in "Mirror, Mirror," "A Private Little War," and "The Cloud Minders."
That, and I have not watched an episode of NBC's
I Spy in some time, but I believed some women featured in location shoots had visible navels, but it was not concealed in various episodes of
The Monkees (another NBC series).