They are not compatible - Peterson's argument is not that neomarxism and postmodernism are natural bedfellows, but that people espousing postmodernist positions

They are not compatible - Peterson's argument is not that neomarxism and postmodernism are natural bedfellows, but that people espousing postmodernist positions nearly always reveal a belief structure based in neomarxism when challenged by an intellectual equal. His evidence is presumably his own conversations with postmodernists, and his theory as to why this is seems based more in a psychological than philosophical framework.