If such distinctions aren't "real," then is the distinction between objective and subjective distinctions itself "real"? If not, if "objective" and "subjective" are not "natural kinds" (of an indefinitely higher order), then the question has no meaning. If "objective" and "subjective" are real, then we can always ask the question as to whether some purported natural kind is more objectively than subjectively delineated, and so by criticism of our theorizing, we can refine our attempts to "carve nature at its joints" so as to make some progress, on some levels, in separating category from category, kind from kind, type from type.
Moreover, there are so many, and such subtle, distinctions, that it would be surprising to find out that all of them are completely "imaginary" (or where does the concept of completeness even come from, then? or the imaginary-vs.-real distinction?). We can differentiate the general from the generic, the indefinite from the infinite, the universal from the general, haecceities from qualitative particulars, sets from multisets and elements, elements from ur-elements and proper classes, types from both tokens and occurrences, extensions from intensions, isomorphism from homomorphism, abstracta from concreta, a genus from a species (and then an individual sample), tropes from properties, sentence-types from propositions, and so on and on. The multiplicity of the universe is even the multiplicity of a conceptual multiverse, and yet then however continuous the gradations might be, that they are gradations that continuously connect things integral on another level is one of the presuppositions of calculus (with its theory of integration), no less.
Since a realist about types of properties need not be of the ante rem class, but can be (as Aristotle mostly was) an in re realist, there is not even a this-worldly-vs.-otherworldly prize at stake. So what is the point of being a nominalist? If things like honesty, evidence, and so on aren't natural kinds either, then the nominalist has no hope of being more honest or evidence-based than the realist, it might seem, and runs some risk of being less sincere/sensitive to proof than their opponents. Or at least of simply, but systematically, talking past those of us who have little-to-no trouble with keeping track of various generalizations and networks of differentiae of objects.
Formative in my own understanding of what might be at stake, here, or rather what the weight of the evidence indicates, has been the SEP article on determinates and determinables. I read it long ago, long before its most recent update, but I will quote from that update nevertheless:
... determinates of a determinable (at a given level of specificity) are both similar and incompatible (red and blue are similar in both being colors; nothing can be simultaneously and uniformly both red and blue). ... For the seemingly distinctive character of determinables and determination may enter into the best case for the claim that there are genuine features of reality that are less than maximally specific—a claim which, if true, has profound implications for a wide range of philosophical issues.
And most applicably:
Two other aspects of Johnson’s discussion are worth noting. First, he denies that determinables are in any sense shared by determinates: “the ground for grouping determinates under one and the same determinable is not any partial agreement between them” but rather “the special kind of difference” (1921: I, xi, 1) distinguishing opposing determinates. As we’ll see, this is a choice point for contemporary accounts.
Ultimately, if the general/particular distinction in general is not "real," then again, there are no particulars for nominalists to believe in, either.🌳 Whether nominalism, pushed to such an extreme that it annihilates the general concept of belief (c.f. eliminative materialism), is thereby self-defeating, might be the inference to make; alternatively, we might say that if agreement and disagreement are not generally inequivalent, the nominalist is not really "defeated" by themselves or by realists, i.e. there is nothing to defeat where there is no battle actually being fought.
🌳Said otherwise: if the natural-kind/artificial-kind difference is artificial, then there are natural kinds just in case we make it so, and since we have made it so, there they are; if the difference doesn't exist, then every kind is neither natural nor artificial, and then either every so-called natural kind might as well be both natural and not natural, or then there is no difference (again) between natural and not natural, and there is nothing to disagree (or worry) about.