I just skimmed Parler’s article, but it seems he operates (like many Bible scholars) under the code model of communication, where words (in this case, nature) have this intrinsic meaning carried by the word itself. So if you get insight into one use of the word, you can transfer that intrinsic meaning to a different use.
In my field, applied linguistics and translation theory, that is considered an outdated way to conceive of how language and communication works. You can’t discover something about how a word is used in Corinthians and apply the “intrinsic meaning” in some mathematical way over to Romans. The prevailing model is the inference model. Hearers calculate meaning based on inferences about what is relevant to the particular context in which they hear something, not be accessing intrinsic meanings of words and adding them up.
The ancient science around hair is super relevant to figuring out what the audience would have inferred when they heard, 'Does not the very nature of things teach you that if a man has long hair, it is a disgrace to him, 15 but that if a woman has long hair, it is her glory? For long hair is given to her as a covering."
But you can’t say, in this verse, because of ancient science, nature means X.
Therefore, in Romans 1:26-27, natural also has to do with X. There is nothing about “hair is genitalia” in Romans. If the main point is just that Paul observed men and women were physiologically different and it is in their nature to procreate together, then I don’t see how that is controversial or informative of anything in the wider debate about Christian sexual ethics where that the physiological differences between the sexes and reproductive capabilities are generally regarded as an obvious fact.