Except that sex is as clear as that Teslas.
There are only two sexes; male and female. If you have XY chromosomes and a penis then you are male or XX chromosomes and a vagina then you are female.
There are a very small minority of people who are born with chromosomal defects or intersex disorders but they are rare. They are not a third sex or a variation. They also have nothing to do with trans issues and have asked to be left out of trans discussions and debates. The majority of people with intersex disorders are not trans and the majority of transsexuals are not intersex.
They also aren't accepting transwomen as such. They are accepting people who identify as women. So, as someone has already pointed out, if a transwomen who identified as a trans woman rather than a woman applied then they would be turned down. However if a hairy bearded bloke applied and stated that they identify as a woman (whatever the fuck that means) they would be accepted.
Biology is important. It's the reason why women are oppressed and discriminated against. Women aren't oppressed because we feel like women or because we're feminine. We're oppressed because of our biology.
Transwomen are not women because the only way to be a woman is biologically. There is no such thing as a lady brain.
Trans people are not oppressed either. They are discriminated against but they are not oppressed because nobody is trying to extract anything from them.
Nobody wants to take trans people's rights away however there are times when sex matters and some places should be segregated by sex and not gender.