Little Hawk:
"No organized religion"?

Well, no enforced religion, but Spock's body got a good send off into space to the sound of "Amazing Grace" supposedly played on the bagpipes by Scotty.

Another episode of the original series had a planet of "sun-worshippers", and it was only in the last few lines that our intrepid star travellers realised that they had been referring to the Son of God.

As to the original question, asking for an earlier Captain of the Enterprise. In Star Trek IV: The Journey Home (the one with the whales) we saw the USS Enterprise of the Twentieth century. We could probably go earlier, but not without going outside of what is considered canonical

CHEERS

Nigel