The case this amicus brief was filed was Drew Adams v. The School Board of St. Johns County, Florida

A TIF had sued her school district under a Title IX claim for the right of a student to access the bathroom that aligned with their gender identity. She won her case before the U.S. Court of Appeals for the 11th Circuit in early August (2020)

The issue at stake is if Title IX's definition of "sex" means solely "biological sex" or includes "gender identity."

The Attorneys General of a number of liberal US state (18? someone can count if they want) filed an amicus brief that I quoted in the OP, which states that the definition of "sex" has changed to:

"present-day understandings of sex recognize that a person’s status as male or female is based on a variety of physiological and psychological traits that do not necessarily equate to external genitalia or the assignment of a particular sex at birth"

A dozen major corporations also filed an amicus brief in support of changing the Title IX definition of "sex" to include "gender identity."

https://www.nbcnews.com/feature/nbc-out/florida-teen-wins-transgender-rights-suit-federal-court-n1236287

I would want a lawyer to step in and explain at this point what this actually means in terms of US law, but suffice it to say that the Attorneys General of a number of US states now believe that the word "sex" as written in Title IX, now legally includes "gender identity."

This means that these learned and extremely powerful Attorneys General are fine to erase women as a distinct legal category under a law, Title IX, that was specifically written to protect women from discrimination in education.

https://en.wikipedia.org/wiki/Title_IX

As I've mentioned, some of the laws that protect women in the US are on the basis of "sex" as is Title IX. That the transgender lobby is not only winning court cases so that those laws include "gender identity" under "sex" but that the Attorneys General of a significant number of US states are now claiming that the legal definition of "sex" has changed to include "gender identity" should frighten every American woman and every one who cares about American women.

In effect, (and again, lawyers please correct me if I'm getting this wrong) the U.S. Court of Appeals for the 11th Circuit has decided what the Equality Act also hopes to accomplish, which is to change the legal definition of "sex" to include "gender identity." My thought is that becuase a higher court has already ruled favorably on the "gender identity" issue, it will make the Equality Act, if it is signed into law by Biden, that much harder to overturn. And again, lawyers please weigh in especially if I'm wrong.