It absolutely does relate to Analytic-Continental feuding - which has far more to do with differences in style, than substance. Lumping in Postmodernism with Marxism, immediately indicates someone not to take seriously, so take care to separate these.
Kuhn should be considered a Postmodernist, and did contribute substantially to the philosophy of science, with his idea of paradigm conflicts rooted in truths held by specific science cultures and communities, and concern for sociology of scientific consensus. But, he went too far, he claimed scientific truths are fundamentally social truths, dependent on which community has power, without means to use cultural dynamics to get to things beyond that. That's because he did not believe truths were fundamentally reconcilable, see his Later Semantic Incommensurability Thesis.
Wider context discussed here: Does postmodernism in art criticism collapse into relativism? What's its merit? The term Postmodernism has generally been defined and used by critics, in a way that ignores the diversity of Continentalist thought. Foucault denied being a Postmodernist, and the term is so often used pejoratively by people who haven't read anything of it that it is more slogan than school.
Foucault, who Kuhn's approach has been compared to, did a similar thing with power. Lot's of interesting analysis finding power dynamics where they hadn't been considered before. But then going to far, and declaring interactions are and can only be about power, inescapably. It takes an interesting mode of analysis, and makes an absurd reductionism & universalising of it - ironically, a metanarrative exactly as postmodernism is typically described as ending, even if it does so by retreating from advocating for shared values into individualist and tribal power dynamics.
Popper wrote The Open Society And It's Enemies, with half of it dedicated to identifying Marx's thought as intrinsically headed towards autocracy, and developing a demarcation of science that excluded historical materialism and Freudianism, which specifically sought to appear to be 'sciency'. Popper was harshly critical of Kuhn's ideas though couldn't dismiss them, organising a special symposium to critique The Structure Of Scientific Revolutions.
Popper, and professional scientists, have to believe that the best science will result in consensus. Based on and justifying, shared values like falsifiability, peer review, and replication. Kuhn sought to challenge the idea consensus will inevitably lead to better truth, and he was right to do so.
But I'd look to Durkheim to correct Kuhn, the binding power of shared values held to be unquestionable must be considered - the controversy over Korean and Chinese human germline genetic experiments isn't about power, it's about what kind of people and community scientists want to be, and participate with. The cohesion of the scientific community depends on that, the internationalism of collaborations, conferences, paper review and publication. Similarly, values about doing reputable truthful science, go beyond power - they become a fitness landscape aimed at challenging cognitive and cultural bias, data manipulation like p-hacking, tobacco-science and greenwashing etc. That is, the core values of the community lead to active accrual of intelligence in enacting them. Kuhn's thought does not have space for that.