Every god figure the Enterprise runs across (and they run across many) is a petulant child, a manipulative jerk, an out-of-control machine or some combination of the above. Every paradise they find is an infantilizing sham or a toxic trap. One of our show's two main heroes is a devil lookalike who says things like, "I, for one, have never believed in angels."Taken together, it's all unambiguously a validation of the religious aspect of American culture that was contemporaneous to when the episodes were aired.
Now, in contrast to that anti-religious strain, what do we get? A reference in one episode to Christmas (a holiday that many atheists and non-Christians observe in some way). Vague references to "many beliefs" and a "reason" for things happening in "Balance of Terror." Concession that a historically determined alien variety of Christianity is socially useful. And a line in "Who Mourns for Adonais" that sticks out like a sore thumb for being lame and out of tune with the rest of the episode's theme.
I'll grant that's enough evidence to concede that the original series is not a full-throated endorsement of rigorous atheism. But that's a far cry from an unambiguous validation of American religious culture--an aspect of American culture that I don't think is any more contemporaneous with original Trek than it is with television today, by the way.