He is a Christian, but he is also an academic...a scientist removed just enough in terms of objectivity to be able to approach the subject as an objective analyst.
Shapiro, like James Kugel (who is one of the finest human beings to have ever lived...and a professor), sounds like he is close to understanding the nature of Christ and that He is a Jew first.
Christians have often really muffed living out the life of Christ, especially in circumstances where they found establishment privilege and could slack off and still survive. That makes for a poor witness.
The New Testament book of Hebrews points back at the Old Testament in many places, declaring the presence of the pre-incarnate Christ in places that modern Christians don’t think a lot about. For example, in the cloud of fire and pillar of smoke that escorted the Hebrews on their way in the Exodus from Egypt to the promised land. Because it’s all but ignored by modern Christians, the chance to talk about it is missed. But Christ isn’t just a “Christmas and Easter” Christ. He would not have been able to apply an Old Testament promise to the Jewish people if that is all He was. How much easier it would have been for me to understand if I could have seen past even Christmas and Easter, even though now I appreciate how important they are.
The outreach of Christ to the gentiles came with the hazard of a poor witness to the Jews. God took all that into account in His plan. And I believe through observation that quietly, many Jews do embrace the spirit of Christ — the same Christ who delivered them from Egypt — as best they can in their confused situation. As is said, a mist in the pulpit is a fog in the pew. The additional story explains some crucial things, but as the Transfiguration example of Moses and Elijah shows, not needed to be understood on earth by those delivered in order that Christ delivers from the power of the Evil One.
I don’t recall Dr. Peterson actually stating that he is a Christian. I have only listened to a what is likely a small portion of what he has said, but I seem to recall him saying he was on a journey to find out if he was a believer. He did say, however, that he LIVES his life as if God is real.