Simple. The phrase "sex-based rights" itself did not even exist before this "debate", and was coined specifically to attack and exclude trans people.
Nonsense.
The point of race- and sex-based civil rights law was to treat everybody the same;
Have a guess when that sentence was written and in which context, Cayeli.
I'll help you out. It's from an article written in 1995 about a disability law proposal and that phrase "sex-based civil rights law" is used entirely without definition or elaboration because the audience is wholly familiar with that term. Given that Ruth Bader Ginsburg made her career arguing about sex-based discrimination that's only natural.
reason.com/1995/08/01/unreasonable-accommodation/
The phrasing "sex-based" and "based on sex" in reference to women's rights has been used in legal discourse since at least the 1950s in the US to give you just one example. Women's rights campaigners have used this phrasing even longer.
Women have been oppressed, discriminated against and disadvanted because of their sex. The fight to redress these inequalities has always necessitated talking about the fact they resulted from our sex being treated as inferior. That's why being able to refer to sex is so important to our rights.
As it is for all other equality issues - if you are not allowed to refer to race, religion, sexuality, disability, poverty, age, you cannot discuss discrimination based on these characteristics. It's impossible to redress such inequalities by denying they exist and are the basis for the inequalities to exist in the first place.