i think a little hostility to abstractions is a good thing for a marxist; i think we've gotten far too comfortable in a set of outmoded abstractions that aren't nearly as useful as they once were. ruthless criticism can't be reserved for our enemies; if we don't subject ourselves to it we risk our practical irrelevance extending to our theories as well.
also ajith's essay is really far more concerned with postcolonialism than postmodernism; it's very easy to conflate the two but i think that's a huge mistake. for one thing, people actually call themselves postcolonialists! you notice very quickly that "postmodernist" is an exonym; very few thinkers actually deliberately call themselves postmodernists. even the guy who invented the term (lyotard) described it as a zeitgeist/universal condition, not as a set of theoretical suppositions. perhaps the root of postcolonialism lies in some ur-postmodernism, as might the roots of french poststructuralism. certainly spivak drew on derrida extensively. then again, spivak spends a good chunk of her time writing about marx and his relevance to postcoloniality. is hauntology postcolonial? if not, is spivak a postcolonialist?
bluntly, most of the marxists who spend their days yelling about postmodernism are just social conservatives waving a red flag. the key is that, invariably, they talk about the "primacy of class" or the need to focus on the class struggle to the exclusion of other, "secondary" struggles like lgbt or black liberation. in doing so, they adopt a definition of "postmodernism" no different to jordan peterson's. obviously, this approach is useless. to quote ajith,
Let us first deal with the “non-class” argument. Caste, gender and
ethnicity (or other social categories) each have their specific characteristics and dynamics. Class analysis does not mean denying this. This is not the meaning of the centrality of class struggle. 131 In fact, developing revolutionary class struggle and establishing it as the central task of all the oppressed demands that the communists must address these specificities in theory and practice. [...] Revolutionary class struggle, the struggle for communism, aims at, “…the abolition of class distinctions generally, to the abolition of all the relations of production on which they rest,to the abolition of all the social relations that correspond to these relations of production, to the revolutionising of all the ideas that result from these social relations.”132 Evidently, without addressing all the relations of oppression in a given society (such as caste, ethnic, gender, national, religious and so on) there can be no revolutionary class struggle.
in spite of this, however, groups like the cpgb-ml and whatever the larouchites are calling themselves use class struggle as an excuse to marginalize precisely these specific struggles that are so vital to the modern revolutionary movement. family, gender, and sexuality are not somehow "apart" from capitalism; they are some of the key components of its system of exploitation and oppression, just as they have been throughout history.
you then have a few communists like gabriel rockhill and losurdo who fixate not so much upon the french poststructuralists (although they come in for some flack) but on the frankfurt school and on post-ww2 western academic marxism. basically, according to these guys, it wasn't state repression and co-option that prevented revolutionaries from seizing power in western europe during the cold war. it was, instead, adorno and horkheimer. using their vast, mysterious, jewish influence they apparently corrupted generations of well-meaning marxists with their utopian anti-communism and dastardly theoretical evil. you often see ludicrous assertions that the whole thing was funded by the cia because horkheimer published one piece in a journal that nobody knew was cia-funded and because marcuse worked very briefly for the cia's predecessor, the oss. they ignored his work because he said they should persecute nazis. also. the founder of monthly review magazine which publishes many of these hit pieces worked for them too. fundamentally, this is just the old far-right ~cultural marxism~ conspiracy theory refracted onto the left. instead of trying to explain why young people are gay and smoke weed, it's trying to explain why they're not joining people's armies. the explanation proffered is, however, the same.
obviously, not all critiques of "postmodernism" are just far-right critiques with the serial numbers filed off, but i think that a critique of postmodernism as such is really the wrong place to start. i think we need to start with what the relevant thinkers actually say. don't talk about postmodernism; talk about derrida and foucault and spivak, and what they actually think and say.