First, not Dr. Thanks, but I’m not a PhD or similarly academically credentialed.
Second, post-modernism is not dogmatic in its precepts, so you can certainly say that a subset of post-modern theorists would find that it supersedes dogmatic Marxist ideology as much as it supersedes dogmatic Christian theology. The variance, however, is that what underlies many of Marx’ books (at least up until the Communist Manifesto) is a clear observation of reality. I tend to like the first half of Naomi Klein’s books quite a bit, but the second half, where she gets into prescriptions for what to do about it I find deeply lacking. That doesn’t invalidate the first half of the work, just the manifesto parts where ideology tends to emerge.
Third, that doesn’t mean you don’t end up with dogmatic post-modernists who end up in silly places. The tiny little War on Science that loomed so large in philosophy departments and was barely noticed in science departments was one such. The theorists attempted to push the boundaries of what was relative and subjective beyond the point where empirical reality was observable and testable, were slapped on their noses with rolled up papers and retreated to their musty dens to mutter into their port.
Fourth, much of the observations of systemic discrimination are in the category of the critique of capitalism or the first half of No Logo. They are clear eyed assessments of reality based on observable and valid things. Post-modernism does not dispute empirical reality (except as with the War on Science, when it oversteps its bounds). Post-modernism per se does not have a problem with the reality of inequity, studies based on it or the like. Some of the more extreme and dogmatic aspects of ideology that arise from inequity studies are anathema to the core of post-modernism. The vast majority of feminists are seeking equality with men, not advancing an ideological dogma of female superiority. Post-modernism doesn’t really have a position against that in the mainstream, but since it’s a schismatic unempirical philosophical school of thought, I’m sure it’s possible to find people considered post-modernists by both themselves and others with every position on this.
Fifth, the point of my article was mostly to help people who don’t think about about post-modernism at all — virtually all centrists and left-wing types — understand more of why a bunch of conservatives thing it’s a gotcha pejorative. The artistic side is what the vast majority of people are actually exposed to, the philosophy, not nearly so much. That a large subset of the right are mischaracterizing post-modernism quite badly, conflating it with things it isn’t, ascribing coherent dogma to it and generally pretending that it’s the resurgence of global expansionary Communism is an interesting social trend but quite opaque to most people.
