Yes, good, thank you. Now we're getting somewhere.
Let's start one level higher, because it's essential context.
Our Constitution defines a Person (capital P) as someone who's been born. If you've been born, you're a Person in the eyes of the law.
And, our Constitution says, all Persons are required to be treated equally, in the eyes of the law. Mostly "the law" means the government, so one could paraphrase by saying the government can't discriminate against anyone.
But the law is more than that, yes? There is for example equal opportunity in employment, equal housing law, and laws pertaining to business offerings from private and public corporations.
The law though, says it's okay to have a blacks only or whites only PRIVATE club, as long as you advertise it that way and never advertise anything different. What you can NOT do is change the terms of the offer after the fact, so if you make a public offering and then deny someone because they're black or gay, that's illegal.
Our Constitution says that all People who are born have guaranteed political rights. It doesn't matter if they're weird or disgusting, they still have equal political rights and must be treated equally in the eyes of the law.
So, as a Supreme Court Justice, it is incumbent on Ms Ketanji to know exactly what constitutes a political Right
Equal treatment under the law is a guaranteed political right. Equal treatment by private institutions is not.
So in this case, we have a conflict of rights. We have an offer, and we also have offers to all the other women.
The question, legally, boils down to "what exactly does the offer say", and if it says "women's swimming", is there a reasonable expectation that this means woman by birth, or is this not a reasonable expectation.
We'll have the Supreme Court providing the answer, but really, my take is, the swimmers themselves should be the ones to answer. I'm sure there will be no end to the amicus briefs.