At some point in DS9 O'Brien makes a reference to religion.
Something like "lord protect us" or a similar expression.
To be fair, expressions like "Oh my God!" or "Good Lord" or "Godspeed" or even "Jesus Christ!" don't necessarily mean that the speaker is religious. They're just common interjections and figures of speech sometimes.
When my printer jams and I blurt "Goddammnit!", I'm not literally calling upon a higher power to condemn a lifeless mechanism to perdition--or expressing a sincere belief in an afterlife! I'm just using, as Kirk put it, "a colorful metaphor."
As for quasi-military thing, Kirk said he was a soldier, not a diplomat, but Picard clearly thought of himself as a diplomat and explorer first and a military man only when necessary. Different perspective, same organization.
I'm inclined to think that Kirk trumps Picard, but I grew up on TOS, not TNG . . . .