Trans people have greater federal employment protection than gays and lesbians do, currently., under a Supreme Court decision Hopkins v. Price-Waterhouse which ruled in favor of a woman not promoted to partner for not dressing femininely enough. Lower courts and the Equal Employment Opportunity Commission have intrepreted that decision to extend to gender presentation by trans employees: if a woman cannot be discriminated against for not conforming to gendered expectations in appearance, neither can anyone else.
There is NO federal law against discriminating against gays and lesbians in employment and housing, though many states have enacted such laws.
Similarly, many states have enacted laws in support of gender identity self id -- mostly along the west coast.
Women's equality was only included in the Civil Rights Act as a joke -- a congressman thought it would be amusing to add "sex" to the list of protected characteristics and would help torpedo passage of the bill. He was wrong. Title VII and TItle IX to the Civil Rights Act are the only laws extending equal rights to women in the US. We do not have Constitutional equality, although we have the right to vote, because the Equal Rights Amendment wasn't ratified by enough states. There simply are not robust legal protections for women in the US.
Nancy Pelosi's Equality Act would add sexual orientation and gender identity to the list of protected characteristics under the Civil Rights Act. What we are seeing, already, are rulings in the lower courts that gender identity presents a greater burden to the trans student than sex discrimination does to female students, and therefore female students must yield rights to privacy etc. to trans students.
The Boyertown case is proceeding through the courts, and there is hope the Supreme Court will hear it and rule that "sex" does not mean "gender identity" and that females have rights to bodily privacy in schools.
(it's very important to understand, too, that both the right to birth control and the right to abortion in the US are predicated on the Supreme Court's ruling that people have a right to bodily privacy. If this right is undermined by rulings in favor of transgirls, it could have spilloever effects regarding the entire premise of the right to bodily privacy, just as the constant refrain that men get pregnant too can have spilloever effects into anti-pregnancy discrimination law and regarding the rights of men over a pregnancy.)
If Pelosi's Equality Act is passed, it will still be illegal to discriminate against women in favor of men in employment, education, and housing. But it will NOT be illegal to count transgirls and transwomen as women for the purpose of demonstrating one has not discriminated against girls and women. And women will lose ALL female set-asides and safe spaces, iincluding prisons and refuges, because we do not have any federal law allowing for certain provisions of sex segregation where proportionate to achieve a legitimate aim.
Already, under the premise that gender identity = sex, we have males winning girls state athletic championships in two states. Since those championships are a route to college scholarships, this is a direct financial hit to females. Expect more of the same, as word of the viability of this move spreads to parents of sons.