Don't take this the wrong way, but this is seriously anachronistic reasoning. I'm going to try to avoid a tl;dr post here, but I'm probably going to fail -- I just gave a 90 minute lecture to my undergrads about this the other day. Yes, human beings have a long history of identifying differences amongst themselves and using those differences to manage and justify various divisions of political and economic power, but that doesn't mean that these historical arrangements functioned akin to our (post)modern conceptions of "race" (and certainly not to the thoroughly modern concept of "racism"). Without even drifting back to the ancient world, consider the differences between the Early Modern understanding of race under much of Spanish colonialism -- where race was viewed as mutable and one could (and, indeed, it was desirable to) "breed out" the "impurities" of Indians over the course of generations* -- with the kind of racial reasoning that would be needed to support the aforementioned opposition to interracial marriage, which generally requires a view of racial groups as both fixed and discrete -- where "blacks" and "whites" are two wholly separate categories of people. (Which is an idea largely formed, at least in the Euro-American context, in relation to the infamous "one drop" policies during the 18th and 19th centuries.) Yes, they both have roughly to do with recognizing difference in phenotype (mostly skin color, in these cases), but they represent radically different beliefs about what that difference means, where it comes from, and how it should govern human behavior. As a brief aside, I'll also point out here that what constitutes phenotypical "difference" is far from fixed, also -- this is entirely too complex to unpack here (google "Irish racialization," though, and you might get some sense of what I mean), but I mention it because it's pertinent to your question about whether or not we currently recognize a difference between in vitro and "naturally" conceived peoples.
As a rough analogy to premodern notions of race and those of our own moment, we might think about the fact that Medieval Europeans also had a conception of "art" that, at first glance, might look like it bears a lot of comparison to the contemporary understanding of the term (both involved displays of skill, music was one of the "Seven Arts," etc.). On the other hand, given the fact that the Seven Arts also included geometry, arithmetic, and logic, we should be keyed in to the fact that this was a fundamentally different way to categorize and organize human knowledge/effort than our own. In both cases (race and art), comparing the pre-modern to the modern is a bit like comparing algae to a redwood: sure, looking at them side-by-side might be useful to garner an understanding of some underlying fundamentals (they both have mitochondria, they both use proteins, etc.), but suggesting that they're the same thing or that the redwood is an inevitable result of algae is surely a fool's errand. When Medievals write about "art," they aren't writing about what you and I think of as art; likewise, when the Classical Greeks or Shang Dynasty Chinese write about "race," they aren't talking about race as we understand the term today. This is what I mean by anachronistic thinking -- suggesting that Classical Greeks were "racist" is like suggesting that St. Francis of Assisi was an "artist."
In any event, there is a bit of a chicken-and-egg argument among historians about the relationship between racism as an ideology and the economic formations that developed under European colonialism (esp. slavery). Marxists/materialists will tell you that it is the distribution of material power during the period that led to the creation of racism as a means to explain/justify that distribution, while intellectual historians would suggest that existing ideas about phenotypical difference (stigmas about dark skin w/in European society, etc.) created an environment in which material exploitation and degradation could thrive. But apart from the serious hardliners in each camp, most of us agree that rather than tackling the question of "which came first," the critical element here is that the two forces were mutually constitutive: racism as a set of ideas and beliefs developed alongside colonialism and racial slavery, and each fed into the other.
All of which means that, to bring us back to the original question: no, I don't find it difficult to believe that if there were significant material and political fortunes at stake in the question of whether or not to grant clones human rights, human beings might develop a system of thought which strips them of said rights. Since you mentioned the Classical period, I'll point out that many Roman and Greek slaves, stripped of human rights, shared the same ethnic ancestry and genetic background as their owners (or those of their owners' peers), and any visibly discernible difference between the two was largely the result of social, cultural, and economic forces (e.g. who was better fed, prohibitions on wearing particular kinds of clothes, branding, etc.). And yet, these societies were perfectly capable of rationalizing away the humanity of their enslaved subjects.
(As a complete and total aside, I'm also inclined to mention that most science fiction, cyberpunk included, isn't really intended as predictive as much as it is descriptive of the contemporary society of its authors/audience. That is, questions about how SanSan citizens treat clones in this fictional universe might be better read as commentary on how the present world treats the disfranchised portions of its population, much as War of the Worlds is pretty terrible guess about Martian first contact, but a pretty accurate metaphor for British contact with India. From accomplished SF author Ursula LeGuin:
"Fortunately, though extrapolation is an element in science fiction, it isn’t the name of the game by any
means....This book [_Left Hand of Darkness_] is not extrapolative. If you like you can read it, and a lot of other science fiction, as a thought experiment... Let’s say (says Mary Shelley) that a young doctor creates a human being in his laboratory; let’s say (says Philip K. Dick) that the Allies lost the second world war; let’s say this or that is such and so, and see what happens…. The purpose of a thought-experiment, as the term was used by Schrodinger and other physicists, is not to predict the future... but to describe reality, the present world. Science fiction is not predictive; it is descriptive.")
*Just to be super, duper clear: I'm not endorsing these Early Modern views or attempting to suggest that they are "better than" the racial ideologies that developed in the 17th-19th centuries: I'm only pointing out that they operated in a radically different fashion.