(I will be basing this answer on a few hundred hours of his university lectures, Bible talks, and his other various appearances. He discusses religion/mythology very extensively, albeit cryptically. So it’s hard to assign him an easy label)
A common mistake is to label Dr. Peterson a Christian. While it’s true the professor has claimed to be a Christian, he should not have done so, as he doesn't subscribe to any of Christianity’s orthodox truth claims (Monotheistic God, Deity of Christ, among most others). Neither is he correct in describing himself as “deeply religious”, since, again, the way he uses the term is vastly different to the way pretty much everyone else uses it.
However, it’s totally understandable why people, who have only surface knowledge of his beliefs, take him at his word. The professor is very well-versed in the Bible, and discusses its stories quite a bit, much like a Christian preacher would. Unlike most classic believers though, He doesn't consider them to be literal truth (edit, comment response: I’m aware much of Genesis and the Bible is almost certainly allegory; this goes beyond that). Rather, he likes to call them a collection of “meta-stories” - ancient stories that evolved over thousands of years by combining the distilled truth out of hundreds of smaller stories until they were finally written down in their final form. Put another way, the Bible, and mythology in general, are the meta-stories that have been “dreamed up” by humanity’s collective unconscious (which is powered in large part by our biology). If you haven’t guessed it yet…
yes, Peterson
has been heavily influenced by Carl Jung
One can totally ignore or redefine the supernatural when interpreting religious writings this way. And for the most part, that’s exactly what Peterson does. We can see this in action in how he interprets the Cain & Abel story. To Peterson, it is not a personal-monotheistic-divine Being that is displeased with Cain’s sacrifice, but society at large. Meanwhile, Cain becomes an archetype of someone who, unable to climb up the social hierarchy, lashes out at the community in a murderous frenzy. A high school shooting is an example of the Cain & Abel meta-story playing itself out.
So religion has given us many good stories that teach us how society functions and the best way for us to function within it. Does Peterson go any farther than this? It doesn't seem so; or if he does, then not much farther. The doctor doesn't hold any concrete views on the existence of a soul/spirit, claiming we can’t know for sure until we understand more about consciousness. Heaven and hell are merely modes of reality that we live through here and now. His answer to whether or not God exists was: “I act as if God exists”, purposefully being vague as he “doesn't like being boxed in”.
EDIT:
More recently, Dr. Peterson, in a debate with Sam Harris, implied that it’s very likely that there is some sort of metaphysical reality that religion has been grappling with, attempting to explain and make sense of. He compared it to Astrology and Alchemy - in the sense of them being flawed precursors to Astronomy and Chemistry. It’s hard to pinpoint what
exactly he means by metaphysical though. It does seem like his views have slightly shifted in various ways since I first wrote the post; but his approach to religion remains primarily pragmatic. While Jordan Peterson does have elements of mysticism in his worldview, he is
not religious, at least not in any traditional sense of the word (or at least not publicly).
In the end, it is much more accurate to simply label him an agnostic. Granted, an agnostic that sees value in the utility of religion, due to a deep understanding of the psychological ideas that religion has in it. But still, at the end of the day, roughly speaking, he’s just an agnostic.