The ravings of reactionaries generally do enough to condemn themselves and so do not require the intellectual engagement of the left, in fact deserving only direct physical and ideological confrontation. In the case of Jordan Peterson however, his hallmark tactic of attacking Marxism by conflating it with postmodernism merits some examination as this tactic is repeated in inverse by opportunists in the “left” who defend postmodernism by linking it with Marxism or by promoting an intellectual convergence of the two. These same opportunists will associate any attack on postmodernism from the left with the ideas of Peterson and other reactionaries, suggesting that Marxists speaking against postmodernism are therefore reactionaries. Marxists must, as Mao put nicely, “learn to play piano well,” meaning we must take on multiple tasks while keeping track of the main one.
Postmodernism with its false progressive veneer presents an internal contradiction within the left, so it must be attacked from the left. Genuine Marxists make no attempt, like Peterson does, to attack it from the right. Clever reactionaries have the skill however to smuggle in their lies with a thin appearance of fact, capitalizing on the general aggravation people have with the postmodernist ideas that are widespread, and Peterson uses this to attack Marxism. The conflation of postmodernism and Marxism is therefore a rhetorical move lending strength to Peterson’s attacks on Marxism. Ironically, postmodernism itself was developed in the academic laboratories of the bourgeoisie for just this purpose—to attack Marxism and replace it as an ideological framework. Since the opportunist misses no chance to accuse Marxists critical of postmodernism of having common ground with reactionary like Peterson, this too must be confronted.
Let us study how Peterson operates. Here he begins by pointing out a shortcoming of postmodernism, only to conflate it with Marxism when he attempts to define the issue:
Postmodernism is essentially the claim that (1) since there are an innumerable number of ways in which the world can be interpreted and perceived (and those are tightly associated) then (2) no canonical manner of interpretation can be reliably derived.
That’s the fundamental claim. An immediate secondary claim (and this is where the Marxism emerges) is something like “since no canonical manner of interpretation can be reliably derived, all interpretation variants are best interpreted as the struggle for different forms of power. 
Peterson himself believes that “the first claim is true, but incomplete,” and his pragmatist conception of truth mirrors postmodern skepticism in denying objective truth, claiming that truth exists only in its social effectivity. This is irreconcilable with Marxism, which asserts that objective truth exists and that there are not multiple ways in which the world can be interpreted or perceived. The only sources of knowledge recognized by Marxism are class struggle, the struggle for production, and scientific experiment. Marxism asserts that there is only one form of power—class power centralized in the state, and not “different forms of power.” The fact that some confused postmodernists claim to follow Marxism does not confirm Peterson’s reactionary conclusion. His conclusion in fact is identical to the postmodernist interpretation of Marxism.
Further, postmodernism does not lack a canon if we understand how reactionaries like Peterson use the term. It has an extensive canon, but teaches this canon as commonsense while discouraging the study of its sources. This is due to the “diffused power” theory, the rejection of authority, and other aberrations inherent to postmodernism. While the average adherent to—or intellectual victim of—postmodernism does not mention Nietzsche, Derrida, Foucault, Spivak etc., in general they rely on these thinkers’ methods and ideas.
Those postmodernists who feign Marxism also have their canon; they might not mention the false Marxists Marcuse, Adorno, Horkheimer and company very often, but they certainly rely on their methods and ideas when challenging the methods and ideas of Stalin or Mao. Postmodernism’s similarities to critical theory serve reactionaries like Peterson in making false links, as well as those reactionaries who are postmodernists claiming to be Marxists in drawing up fraternal bonds and affections between the two opposed ideas of the world.
Peterson of course has no interest in scientific clarity on either postmodernism or Marxism, and he makes use of a false critique of the first—sprinkled with what looks like bits of truth—to oppose the second, to debase it of its class character and to diminish its appeal by associating it with the kvetch that is postmodernism. Marxism on the other hand is a weapon, a fighting idea.
While conceding the irreconcilability of postmodernism and Marxism, Peterson—the irrationalist that he is—still insists on saying that the main theorists behind postmodernism were “soaked in those [Marxist] patterns of thought.” He does this by suggesting that the questions of power and social struggle link them.
However, Marxism sees class struggle as rooted in the historical struggle for production which exists objectively in the contradiction between the forces and relations of production, and it asserts that power is class power and fused around class rule. Postmodernism instead poses social struggle as essentially individual and rooted in subjectivity, not objective historical development, and views power as diffused while refusing to answer the question of power for whom. These are diametrically opposed viewpoints, with irreconcilable definitions of what power and social struggle are. Peterson exhibits a vulgar and ridiculous combining of two opposites into one. His illogical position implies that power is non-existent—this is essentially the same thing as diffused power but with a different conclusion, because they cannot actually comprehend power materially and instead treat it as imagined. Peterson’s ideology and postmodernism are therefore identical insofar as they present a bourgeois and metaphysical view of society.
There are deeper problems as well. For example: Postmodernism leaves its practitioners without an ethic. Action in the world (even perception) is impossible without an ethic, so one has to be at least allowed in through the back door. The fact that such allowance produces a logical contradiction appears to bother the low-rent postmodernists who dominate the social sciences and humanities not at all. Then again, coherence isn’t one of their strong points (and the demand for such coherence can just be read as another patriarchal imposition typifying oppressive Western thought). 
The fact that postmodernism is constantly at odds with itself is not a unique feature of postmodernism but one it inherited from liberalism, including the liberal pragmatism lauded by Peterson. This however does not translate into a lack of ethic; rather, postmodernism uses ethic to promote itself, and in all cases claims to be a more valid form of identifying and assigning ethic than Marxism has been historically, and herein lays its appeal especially to younger generations. Any deformed liberalism which rejects totality will be at eternal odds with itself, but every one of these micro-groups at war with the other is based on an ethic; each micro group must have an ethic with which they justify their warring against the others.
Marxism for its part is quite ethical and has a better total ethic than postmodernism could ever hope to replace because the former recognizes that ethics and morality have a class character and so distinguishes between bourgeois and proletarian ethics and morality. Hence Marxism is at war with the other persistently and not at war with itself as is the case with postmodernism.
The reactionary pseudo-intellectual Peterson concludes his parlor tricks with a confounding statement and a sad shrug:
Postmodernism, by its nature (at least with regard to skepticism) cannot ally itself with Marxism. But it does, practically. The dominance of postmodern Marxist rhetoric in the academy…attests to that. The fact that such an alliance is illogical cannot be laid at my feet, just because I point out that the alliance exists. I agree that it’s illogical. That doesn’t mean it isn’t happening. 
Marxism and postmodernism are not allied, and cannot ally practically; both will necessary struggle over the same terrain, among the same masses. The ideas of the masses are a battleground between proletarian and bourgeois ideological influence. For that matter, reactionary ideas like Peterson’s—which lack the grace possessed by postmodernism to at least attempt to conceal its reactionary identity—are also active in the field of ideological struggle among the masses. To defeat these ideas, the single worst thing a Marxist could do would be to attempt to defend postmodernism, to shelter it or to allow it any ground.
For Marxists, the ideological enemy is bourgeois ideology—no matter what kind of hat it is wearing that day.
 Jordan Peterson,Postmodernism: definition and critique (with a few comments on its relationship with Marxism). Available at:https://www.jordanbpeterson.com/philosophy/postmodernism-definition-and-critique-with-a-few-comments-on-its-relationship-with-marxism/