Some facts about Jordan Peterson:
One of his major lines of argument, in the talks he gives and the articles he writes, is that there is such a thing as "Cultural Marxism"- an attempt, as Peterson argues to turn the United States, Canada, the UK or the parliamentary democracies of Europe and Australia/New Zealand into dictatorship on the model of the Soviet Union under Stalin.
To do this, Peterson uses the term "Marxism"- which simply refers to form of economic analysis and a broad set of predictions of how an eventual socialist or small-c communist future might come to be- as a synonym for Marxism-Leninism, the term Stalin coined to codify his unnecessarily repressive and bloodthirsty methods of ruling the USSR into something like an actual ideology, rather than simply his chosen method of taking and maintaining political power.
The antiracist/cis-feminist/LGBTQ+ rights/ Indigenous solidaraity/Immigrant justice causes are not synonymous with "Marxism". "Marxism" is not identical to Marxism-Leninism, and it is deeply inaccurate of Peterson to imply that any structural change in any "Western" society will inevitably lead to police state repression, secret police hauling people off in the night for interrogation, torture, long sentences in slave labor camps, or summary execution.
Peterson is also known for refusing to respect the pronouns of his students in the days when he was still a professor of psychology, and for claiming that, if a proposed law in Ontario barring discrimination based on gender identity in that province were to pass, he could actually be imprisoned for misgendering a student- this is not factually correct: under the law, the only grounds under which a person could be tried and convicted and receive a prison sentence would be if they called for genocide against transgender/non-binary/Two Spirit/gender-fluid people-