The Genealogical Adam argument seems to run into its greatest trouble on the topic of pre-Adamic (or non-Adamic) humanity. While I am not ready to declare pre-Adamism to be heresy just yet, it is certainly far outside of the mainstream readings of Genesis. I would put the notion under two tests.
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Is there any indication that pre-Adamism falls within the bounds of acceptable thought in early Christianity and Judaism?
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Does pre-Adamism pass the essential test of the Rule of Faith?
For the first question, I have certainly found evidence that early Christians and Jews felt a certain discomfort about some of the background characters in the first several chapters of Genesis. This arises most often with regard to the quaestiones of where Cain got his wife and who was trying to kill Cain. Jubilees 4:9 invents a sister for Cain, named 'Awan, whom he marries. As is the modus operandi for the author, details are invented when there is some sort of difficulty in explaining the text. Philo, Quaestiones in Genesim 1.174, recognizes this as one of the standard questions that arises in the study of Genesis and provides multiple explanations for those who might try to kill Cain: nature, wild animals, or Adam & Eve. It is Philo’s tendency to provide as many interpretive options as possible. It is interesting that he either does not know or has rejected the tradition that these people are siblings and other close relatives of Cain. Pseudo-Philo, Jewish Antiquities 2.1-2, invents a wife for Cain named Themech but does not explain her origin. Josephus makes allusion to this debate in two places. In Jewish Antiquities 1.59, he mentions Cain’s fear of the wild animals, perhaps revealing that he knew the same tradition as Philo. In Jewish Antiquities 1.52, he also mentions daughters born to Adam and Eve, showing that he knew a tradition similar to that in Jubilees. He may have avoided discussing the tradition directly, for fear that his Roman audience would be appalled by such incest. Targum Pseudo-Jonathan 4:1 (8th century CE, but likely preserving older material) claims that Cain is the son of the angel Sammael and Eve. He later marries his half-sister (born of Adam and Eve). As you can see, this question was certainly under discussion in this time period, and there is not a single, dominant interpretation. A wide range of speculation was considered within the bounds of what was acceptable, but none of that speculation (as far as I know) ever led specifically to a pre-Adamite hypothesis. In the rare cases where a non-Adamite is involved, it is a supernatural being rather than a human one. A similar study could be made of early Christian approaches to the same question, but I have not gotten deep enough into it to reach any more than preliminary conclusions.
As far as I know, the earliest instance of Christians or Jews speculating about pre-Adamism is found in the Judaism of medieval Spain. Yehuda Halevi and Maimonides both discuss the hypothesis, but the topic may have arisen under Islamic influence. Within some fringe Muslim groups (like the sufis) a pre-Adamic speculation existed. The fact that pre-Adamism is not seriously considered apart from Islamic (and heretical Islamic at that!) influence raises several red flags for me.
The second question is whether a pre-Adamic doctrine would violate the Rule of Faith. In other words, is any part of the clear and universal doctrines of historic Christianity contradicted by a belief in a pre-Adamite humanity. This is more difficult to answer because the idea is so new to me that I have not yet traced out all of its implications. I know that @swamidass takes great pains to show that the possibility of pre-Adamic human beings does not necessarily undermine the historicity of Adam or the doctrine of original sin. If he had not done so, then I would have certainly rejected the notion. I would be very interested to hear the reflections of others on this question.