1-Those words were spoken by a man not of faith.
2-Those words were spoken by a man who was not of faith.
3-Those words were spoken by a man who was of faith.
They look incorrect to me. I think ‘1’ and ‘2’ would work if it was followed by something like: ‘but of reason’.
It may sound a little awkward, but this actually echoes the language of the King James Version of the Bible, the standard Bible in English for about 450 years. Romans 14:23 says “for whatsoever is not of faith is sin.” While that language might be slightly archaic, it still is suggestive because of the long history of the Authorized Version. A modern version would probably say something like “whatever is not done in faith is sin.”
If you are familiar with the Bible, then you know that Romans is one of the New Testament books that emphasizes salvation by faith in Jesus Christ, not by doing or avoiding specific works. The context is a dispute in the Roman church about eating meat. The author’s response is that the specific work of abstaining from meat is not the issue, but whether either action (eating meat or not eating meat) is done in faith.
Anyone who is seriously studying the English language, especially its literature, should be familiar with the King James Bible (a.k.a. the Authorized Version) because it is alluded to so frequently. It often has nothing to do with the faith of the author, but that the King James Bible has just been a part of the culture for so long.