Jordan Peterson is a mixed bag. On one hand he is correct in his critique of Postmodernism, but on the other hand he has not read the actual works of Postmodern theorists. He is critiquing a phenomena he doesn't fully understand.

He is correct that Postmodernism is trying to replace the Modern value system of the Enlightenment with a new value system. But, he doesn't fully understand what this new value system is.

Your assertion that Peterson is expressing his shadow is not correct. Peterson believes in Jung who was a transitory figure between Modernism and Postmodernism. Jung believed that social structure was based on myth and archetypes. This is a transition between the objective world of Modernity and the socially constructed world of Postmodernity. Peterson is constantly expressing the 'structure' of Jung, and fighting against the 'post-structuralist' ideologies of Postmodernism.

The people who hate Peterson believe in 'Postmodernism' as a political theory. Peterson is correct in the idea that Postmodernism focuses on social power as a system of values. He is correct that basing a value system on "Power" is very dangerous. Not a "conspiracy theory". It is a real problem.

I wrote an essay on the dangers of Postmodernism here: https://jaime-roberts.medium.com/the-hyperreal-world-of-postmodernism-93f1130f55f0