Let me preface this by making unequivocally clear the Jordan Peterson (if we start insisting on titles, call me Hofrat commiespaceinvader) is a complete hack who publishes fascist mysticist drivel and where the person who strongarmed him through the committee for professorship regrets doing so now. If he wants to stick to Jungian metaphysical non-sense, he can do so for all I care but he should stay away from history, society, and even lobsters.

That out of the way, /u/Georgy_K_Zhukov has written about this question before in the previous linked answer as well as here where he covers the Nazis' claims on the old testament and the German Church. What I want to add to this is a bit of intellectual background history and in order to do so, it is imperative to start with the German nationalist movement in the 19th century and its more radical off-spring in the völkisch movement.

Now, a crucial bot of context for this is that German united rather late under one nation-state in the classical sense with Bismarck's policies following the Franco-Prussian war in 1871. Prior to the Napoleonic wars especially, there had been a whole slew of German states under authority of the Church, including the prince-bishopric Cologne, Mainz, Trier and so forth. While these forms of rule ended with the Napoleonic re-organization of the German states and wasn't resurrected at the Congress of Vienna, the Catholic Church as an institution retained a strong control on institutions of education and social care and through these, political power. German nationalism as it developed in the 19th century took a strong position against this power.

Both welfare and especially education are prime tools in terms of nation building and spreading general national consciousness, especially when standardizing language and teaching it to subjects. Additionally, the Catholic Church was one of the prime supporters of the rule of the Habsburgs, who were the prime opponents in the eyes of German nationalists in the 19th century for their rule over a multi-ethnic, multi-language empire was understood as antithetical to German unification. When the Habsburgs were some of the prime suppressors of the 1848 attempted national revolution, this status solidified and German nationalists of every coleur started agitating against the Catholic Church.

Within this specific campaign, a rather specific view emerged: The Catholic Church was an international institutions and hence the opposite of the national ideal. Whereas in the eyes of the nationalists, there should only be one single focal point of individual loyalties – the nation –, the Catholic Church represented a problem in that it provided an additional focal point that was essentially in competition with the nation for loyalty.

When after German unification, Bismarck started the campaign of the "Kulturkampf" (culture war) to wrestle control of key institutions from the hands of the church into the hands of the state, the whole campaign was underlined by this kind of rhetoric: Catholics were by fiat of them belonging to the Catholic Church suspected of not being loyal to the nation. Would they receive their orders from Berlin or from Rome, was a question frequently asked during these times.

And for the radical offspring of German nationalism, the völkisch movement, this became a central tenet of their ideology. For the German Volk to succeed in the historic struggle of races, it needed to defeat its internationalist/globalist enemies: Jews, the Habsburgs, Communism, and the Catholic Church. As Jörg Lanz von Liebenfels, one of Austria's most prominent völkisch thinkers put it in his propaganda ditty: "Ohne Habsburg, Juda, Rom bauen wir den deutschen Dom" (Without Habsburg, Juda and Rome, we build the German Cathedral)

This conflation of all international/globalist forces that ultimately lead to the conviction among the völkisch ideologues that Communism, Habsburg, and Rome were all tools in the hands of the international conspiracy of the Jews, was especially prevalent in Austro-Hungary because of the German nationalists there embracing an essential völkisch position in their opposition to Habsburg rule over multi-ethnic territories instead of unifying the German people under one banner. And once again, seeing how closely tied together Habsburg and the Catholic Church were, lead to a notable radicalization of Austrian völkisch thinkers.

Enter young Adolf Hitler. Now whether or not Hitler during his time in Vienna really read all the stuff Liebenfels and other anti-semitic and anti-Catholic thinkers printed at the time, is not clear but given how strongly they are referenced later in Mein Kampf, it is a safe bet that Hitler at some point familiarized himself with the Austrian völkisch tradition that massively influenced his further thinking, including its position against the Catholic Church.

However, being opposed to the Catholic Church from a völkisch standpoint is not the same as being anti-religious. Peterson mentions Marxism in his little sentence that is so shallow as to have become entirely meaningless up there. Lenin, whose position in Marxism was a rather influential one f.ex. argues regarding religion in Socialism and Religion:

Everyone must be absolutely free to profess any religion he pleases, or no religion whatever, i.e., to be an atheist, which every socialist is, as a rule. [...] So far as the party of the socialist proletariat is concerned, religion is not a private affair. Our Party is an association of class-conscious, advanced fighters for the emancipation of the working class. Such an association cannot and must not be indifferent to lack of class-consciousness, ignorance or obscurantism in the shape of religious beliefs. We demand complete disestablishment of the Church so as to be able to combat the religious fog with purely ideological and solely ideological weapons, by means of our press and by word of mouth. But we founded our association, the Russian Social-Democratic Labour Party, precisely for such a struggle against every religious bamboozling of the workers. And to us the ideological struggle is not a private affair, but the affair of the whole Party, of the whole proletariat.

That is a pretty clear position that takes issue with religion itself – as a "bamboozling of the workers". Nazism on the other hand, takes specific issue with the Catholic Church as an international institution – and issue they were happily able to put aside to make a deal with the Vatican to finance religious institutions in Germany with tax payer money. Hitler's and the Nazis' issue was not with religion per se the same way, Lenin had an issue with the system of religion as a whole. Himmler f.ex. in his attempts to re-introduce some esoteric mubo-jumbo that he identified as the "original Germanic religion" can in fact be called a highly religious man with a passion for his pseudo-religion. Similarly the existence of the German Protestant Church as a sort of religious extension of the the Nazi party bespeaks the fact that the issue with religion as far as the Nazi regime was concerned only extended to organized institutions not under their control.

The simple fact of the matter is that these North American debates about whether the Nazis were atheists or Christian, completely fail to grasp the complexity of the situation and the relationship between Catholics and Lutherans, German nationalists and völkisch ideologues and the situation regarding the Catholic and Lutheran Churches in German of the 19th and first half of the 20th century. Nazi Germany was neither an atheist boogeyman – it wasn't even a declared atheist regime like the USSR – nor was it guided by Christianity as an ideal. But such complexity seem too much to bear for peddlers of reactionary nonesense like Peterson.

There is definitely room to say more, but you might be interested in this earlier thread in which /u/Georgy_K_Zhukov discusses the appropriation of Christianity by the Nazi Party and Nazi theologians, and by the earlier völkisch movement--and some of the theological machinations that retaining Christianity required:

• How did Nazi (or any anti-semetic) Christians view the Old Testament, given that pretty much exclusively follows the history of the Jewish people?

A quick historiographic followup question :

What's your opinion on Karlheinz Deschner's God and Fascists from 1965, and its take on actions of the Church officials in Nazi Germany and their exoneration by Adenauer administration after the war - Given the age of that book, and the fact that these exonerated people at the time were still alive and active contributors in FRG's public life, how accurate is Deschner's book?