There were a few references that could be taken to indicate a religious position.I don't remember anything in ST that implied that the crew were not religious; it's just that we never saw any reference either way.
For example, when Kirk was dealing with Apollo, he said that they had no need of gods because "we find the one quite sufficient." That could imply that it is commonplace in the Federation to believe in God, or at least that Kirk does. Also, there is a chapel on the Enterprise. While that need not necessarily be religious in nature, the term "chapel" does traditionally suggest religious, particularly Christian, use.
And, of course, in "Bread and Circuses," they make references to Jesus Christ and don't seem to be doing so in a negative light. Certainly, they seem to view the coming Christian transformation of the planet as a good thing, as opposed to Picard's negative view of religion in "Who Watches the Watchers."
There's no clear evidence to indicate that any of the TOS crew members are religious, but there are some suggestions that some of them might be, and certainly no evidence to indicate that they are not.