QuiteContraryMary made some of these points, but since I wrote this I might as well post it, in case anyone is interested.
Today's NYT report is centered on a big lie. The 1972 federal law in question, Title IX, deals specifically with discrimination & accommodation based on sex in education (& education-related activities like school sports) in public & private educational institutions that get federal funding. Contrary to what the NYT says, Title IX does NOT mention gender or gender identity!
Similarly, the US Civil Rights Act of 1964 prohibits discrimination based on "race, color, religion, sex, or national origin." There's no mention of gender or gender ID, though various courts have decided in recent years that in many cases the prohibition of discrimination based on sex also includes sexual orientation.
Just as the GRA in the UK had to be passed by Parliament, & changes to it would also have to voted on by Parliament, in the US a federal law dealing with gender & gender ID would have to be passed by the US Congress. But Congress has not passed - or even proposed - any federal laws pertaining specifically to gender or gender ID, so there is no US equivalent of the UK's GRA. And there probably won't be because the US constitution leaves as much law-making & rule-making as possible to state & local governments.
Obama tried to circumvent Congressional, state & local authority by sending threatening "advisory letters" to US educational institutions that by fiat proclaimed that where Title IX mentioned sex, it really meant gender & gender expression/ID. This huge overreach was probably unconstitutional; IMO it was an egregious abuse of power. An analogous action would be for the UK PM to simply announce she's putting the proposed changes to the GRA into effect tomorrow, decreeing that "trans women are women, get over it" & excluding input from the public & Parliament entirely.
Obama's overreach enraged not just the right-wing, but also many feminists. Now the Trump admin is simply rescinding Obama's executive orders/letters & re-asserting that federal discrimination laws as originally & currently written specifically speak of sex, not gender & gender ID. But most people are not well-informed enough to know the difference, leaving the field open for TR propagandists to shriek "we're being defined out of existence!"
Unfortunately, there has been no national debate about gender ID & transgenderism in the USA, which is one of the reasons I (& I suspect others from the USA) have become such avid followers of what's going on in the UK around the GRA - & such big fans of all you UK women fighting self-ID. (Kudos & thanks.) Given the political climate in the USA today & the rapid inroads transgender ideology, lobbyists & organizations have made amongst the Democrats, the left, universities, & the MSM, there will probably will not be any reasonable, reasoned national debate about it here for a very long time - if ever.