In some ways, this is avoiding your actual question, but I do want to point out that some form of genealogical relationship between man and ape (or monkey) was proposed long before the theory's scientific expression in an evolutionary context. Thus, for example, the late sixteenth-/ early seventeenth-century philosopher Lucilio Vanini:

Other [philosophers writing on the origins of mankind] dreamed that the first man was born from the rot of apes/monkeys [simiarum], of pigs, and of frogs, for they are similar in flesh and in character.

In other words, Vanini is saying, apes and monkey resemble humans both physiologically and behaviorally. (This latter point would have been familiar to most of his contemporaries; indeed, the monkey's behavioral similarity to humans had made it a stock figure in folk tales for centuries by Vanini's time.) And the easiest way of explaining this similarity is through a semi-genealogical relationship in which man is born out of the putrescence of his progenitor species, much like flies, worms, and other creatures were believed to be spontaneously generated out of putrescence. But Vanini continues:

Some of the milder atheists, however, say that it is only the Ethiopians who came forth from the genus and seed of simians, for the same color is seen in both.

Now, setting aside the outrageous racism for a moment, we might note that the mention of seed here makes this an even more explicitly genealogical theory: Ethiopians are descended from simians via sexual reproduction. But it's difficult to overlook the elephant in the room for too long: the awkward truth is that while some theories of the relationship between man and monkey were universal, many applied the relationship only to certain stigmatized portions of humanity—often Black people.

We may see, for example, a somewhat similar narrative put forth in the Greater Bundahishn, a Zoroastrian text probably composed around the ninth and tenth centuries CE but which made great use of older materials. In the Bundahishn, Black people are once again equated with apes, but the relationship is not directly ancestral. Instead, the two groups are similar because they were conceived in similar ways, as products of transgressive coupling between humans and demons:

The [Avestan text] says, too: "Yim, when his royal glory departed from him, took a female dēw to wife, and gave his sister Yamig to a dēw to wife, because of his fear of the dēw; the apes, the bears, the forest-inhabitants, the tailed ones, and other noxious "sorts" [species] arose from them; and his [Yim's] lineage did not progress therefrom."

Regarding the Black people, the [Avestan text] says: "During his sovereignty, Až ī Dahāk let loose" a dēw on a young girl and let loose a young man on a parīg, and they (the female counterparts) had sex with the visible image of the male (counterparts of each other); through this new way of the action the Black people appeared."

So here, while Black people and apes are not understood as being formally related to one another, there is an argument that both are generated by similar processes which explain their common features; and the half-human genealogy of both groups is used to explain their resemblance to the rest of humanity while still keeping them at a remove. It has suggested that this passage may have been composed during the Zanj rebellion against the ʿAbbasid caliphate (868-883 CE), which may explain why Black people were singled out for special abuse in the text.

Another tradition casts the relationship between monkeys and stigmatized people in the relationship of transformation, rather than genealogy. A talmudic tradition attributed to Yirmeya bar Elazar (2nd century CE) posits transformation into "apes, and spirits, and demons, and female demons" as a punishment that befell one group of the builders of the Tower of Babel (Sanhedrin 109a). This may in turn have influenced Islamic legends in which Christians and Jews were transformed into apes and pigs as a form of divine punishment (a process known as maskh). Thus, for example, a group of Israelites who have collected fish from the sea (among other prohibited activities) on the Sabbath are admonished: "You know of those among you who have broken the Sabbath; We have said to them: 'Be abject monkeys!'" (Qurʾān 2.61-65, 7.166).

Unlike the examples of Vanini and the Bundahishn, these transformational accounts did not rely on a genealogical link between man and simian. Instead, the link is hierarchical: man can transform into simian because the two groups are relatively close to one another in a hierarchy of animals (though man is, of course, decisively on top). This hierarchy in many ways resembles the Great Chain of Being used to arrange living things in the Christian world, which similarly places apes on just the next rung down from man. In these cases, the similarity is due to the fact that the simian is by nature an almost-human, falling short of the ideal in its lack of a soul or morality or some other characteristic. Morally lapsed humans divest themselves of this essential characteristic, and are thus liable to fall a rung lower in the chain. What is important here is that this status was not exclusive to monkeys: pigs, lizards, and bears, for example, were also considered transformative animals in Islamic sources.

Thus, at different times and in different cultures, the relationship between man and monkey was conceived as directly genealogical (Vanini), analogously genealogical (Bundahishn), or hierarchical (maskh stories and the Great Chain of Being). There was no constant rationale for this relationship, but the recognition that the two animals are fairly similar was something of an enduring trope in philosophical and theological literature.