Complementarian thinking largely draws on natural law as its general foundation. But grace does not destroy but supports and perfects nature. And so the church, the new creation by that special revelation in Christ, maintains this distinction in the church (e.g., in 1 Tim 2).
In the 1980s, American evangelicals (mostly of the Baptist persuasion) built a foundation for complementarian thinking on the key passages in the NT that affirmed the male-only episcopate & particular roles in marriage. They also used biblical passages that overlapped w/ natural law (since the revelation is practically one).
This meant that the basic foundation of sexual difference, while not ignored, was not emphasized. The following decades then saw scholars and pastors and people disagree over the interpretation of specific passages as well as hermeneutical approaches to Scripture.
In the last few years, however, American evangelicals have awoken to the notion of natural law since many now declare that their gendered identity does not match their biological sex. So it’s more obvious that God’s law in nature needs reaffirmation.
And it is obvious, I think, that evangelicals are realizing that their 1980s version of complementarian thinking forgot what all prior Christian thinkers had known: natural law defines the general difference of the sexes while special revelation provides the specific application of that difference in eschatological ministry (i.e. the church).
In 2020, I published an article that aims to show how natural law lays the foundation for distinguishing the sexes. You can find it here. I still think my argument there makes sense, although I believe I could improve upon my presentation were I to update it today.