Do you really try to sell the idea here, that the Bible "invented" the moral code we follow today?
Cause that's how I understand what you are saying.
That what we understand of our moral system today is rooted in Middle European culture which was a religious one for centuries is true.
But in no way are we feeling bound to the BRONZE AGE morals that are written down in the bible.
In fact many of those morals are considered immoral today.
Examples are: stoning unruly children to death, putting homosexuals to death, slavery is ok and encouraged, women being the property of men (literally),...
We consider these things immoral today DESPITE the church having so much power over our society.
We dragged the church with us into modern times kicking and screaming, forcing them to adapt.
Church leaders would never have jettisoned laws from scripture on their own as they have to consider everything in it as the word of god.
As society moved on and learned better ways those laws became subject to interpretation.
On the core subject of the thread, I really don't see this concept working, just doesn't jive with the secular nature of the concept of Star Trek.
It would be interesting to do an episode or a small arc around this concept as a source of dramatic conflict, sure.
It would reflect a social controversy of the real world, in fact the very same discussion we have going here and in that sense be a very Star Trek theme to explore.
But no way this would carry an entire series and still keep it consistent with what is established about the Trek universe.