Although he says Peterson intends to release the whole interview on his own podcast, so far, I haven't seen it. (If someone knows where it is, please let me know!)
Bp Barron calls Peterson a "bridge figure" from materialistic secularism to religion. I would say that Peterson goes somewhat farther than that -- I certainly wish I'd had him as an undergraduate professor, although I don't think he would have existed in the intellectual climate of that time. He is a leading figure in the so-called "intellectual dark web", which includes an unserious atheist, Sam Harris, but also other figures like Carl Benjamin who, although we might say they are sentimentally materialist, are sufficiently if unconsciously rationalist that they can approach Aristotelian and even Thomistic conclusions.
Prompted by Barron to outline his views on religious belief, Peterson says, starting at about 5:35
I didn't really feel that I had the moral right to make a claim about belief in God -- I mean, that's not a trivial thing to, to, let's say, proclaim, you know, because it's not really a matter of stating in some verbal manner that I am willing to agree semantically with a set of doctrines. It means that you have to live -- you have to commit to living a certain way, and the demand of that life is so stringent and so all-consuming, and you're so unlikely to live up to it, that to make the claim that you believe, I think is a -- to me, it smacks of a kind of -- I mean, I understand why people do it, and this isn't a criticism of people's statement of faith, but for me, the critical element of belief is the action and the requirements of Christianity are so incredibly demanding that I don't see how you can proclaim yourself a believer without being terrified of immediately being struck down by lightning or some cosmic. . .This is somewhere at the threshold of Thomism, and in what I currently wish I might have had as an undergraduate curriculum, a Peterson-like figure would express a set of secularist dilemmas (like the one that's driven Peterson's career, the problem of 20th-century mass murder), with an Aristotelian-Thomistic rationalism gradually inserted.
The answer to the dilemma Peterson poses here, and it's a real dilemma, and something that remains a dilemma in a conventionally secularist academic environment like Peterson's (where he, let's face it, is not comfortable), is divine mercy and divine grace.
I would imagine that could be covered later in the undergraduate curriculum. But I often come back to Peterson's YouTubes.