First Queer Theory picked it up. I believe Judith Butler was the first person to argue GI has an objective real existance (in as much as critical theory believes anything really exists). Butler's work is really the intellectual driver for this movement.
Weirdly, Butler’s work - which isn’t really queer theory at all - actually argues the opposite! Her work on gender and sex (in “Gender Trouble”), originally argued that gender was the mere performance of tropes and gestures, and that “gender performativity” is a way of destabilising gender stereotypes. Her original work actually tries to undermine the very idea that gender is fixed or innate.
But it was taken up in a very reductive and simplified way, largely in an enthusiasm for the idea that drag and cross-dressing somehow subverts and liberates people from gender (rather than just remaining a performance). She herself has gone along with the TRA enthusiasm for her work by deliberately backtracking on what she originally wrote.
“Queer theory” is a bit of a misnomer, as most of the original “queer theory” texts of the 90s were nothing like today’s transgender or gender ideology, and largely were exclusively about the history of the gay male experience and “queer” as a gay male identifier (eg. in Eve Sedgwick’s famous Epistemology of the Closet). The kind of gender theory stuff that began circulating on social media like Tumblr and Twitter in the early 2010s bears very little resemblance to “queer theory” at all, and is more like just bad identity politics for teenagers. Moreover, it gets any gender studies or queer theory it does reference invariably totally wrong and backwards.
So I tend to think of the transgender ideological juggernaut as something which has actually co-opted the idea of queer theory and gender studies, and warped it, rather than the reverse. Because when you actually read the works that were part of that 1990s judith of queer theory, they actually tend to argue the reverse to current gender ideology rather than be aligned with it!