Women who undergo mastectomies and hysterectomies are still women. Men who lose their testicles to injury or to testicular cancer are still men.
You're right - women who undergo mastectomies and hysterectomies remain women no matter what. Men who undergo orechtomy or phallectomy remain men.
There is the absolute biology, the chromosomal array that is associated with male and female and there are many variations on that one standard allotment of an X and a Y or two X's. There are intersex individuals; there are hermaphrodite individuals--rare, but still existing.
People with disorders of sexual development are still either male or female. Karyotype variances are sex-specific. And true hermaphrodites, in the biological sense, do NOT exist among humans (nor among any mammals). No human has the ability to produce BOTH sperm and eggs. No human has the ability to fertilize themselves. There's a lot of casual use of technical language that happens with these discussions, and we really, really can't mix them up. You can't use a casual version of 'hermaphrodite' as meaning a person with ambiguous genitalia at birth when also discussing genotypes and the biological functioning of sexual reproduction.
There are only two sexes among humans - male and female. No human is any other sex, nor is any human both sexes, nor is any human some in-between sex. Each individual's sex is ultimately determined by the type of gamete around which their reproductive anatomy is arranged. Even people with DSDs have anatomies that are ultimately arranged around the production of sperm or the production of ova... even if they are not able to actually produce those gametes.
There are individuals who have never, ever felt comfortable as the sex they were presumed to be at birth but who have always felt as though their true self was always the other sex. I've known such people. It's not fake. It's not for attention. It's not mental illness. It's how they perceive themselves and how they wish others to see them. Don't we all wish to be seen as our true selves?
I respect you, Toni, but I disagree here. Yes, people with deep-seated gender dysphoria do exist. It's an unenviable condition, and I have immense sympathy for people with that condition - my sister's oldest child is one. But whether they subjectively feel uncomfortable with their sexed body, or if they genuinely feel like their "true self" is the other sex... their true self is inextricable from the body in which their brain resides. Unless you wish to posit the existence of a soul as being separate from the body, then we're going to be at an impasse here. I do not believe in souls, and I definitely don't believe in gendered souls that the magical sky-daddy accidentally stuck in the wrong body. I do believe that people can have delusions, and that people can have neurological disorders that disrupt their perception of themselves. Whether you wish to view that as a mental illness or not is up to you - to me it is entirely irrelevant. A male is a male is a male. A female is a female is a female. No matter how strong my <nephew's> dysphoria, no matter what lengths they go to to present and live as if they were a woman, they are NOT a woman, and they never can be. Luckily, they are also intelligent and caring, and they accept this reality. I will call them by their chosen female name, because I love them dearly. But they are well aware that they are still male.
How people perceive themselves is much, much more complicated and has to do with a lot more than chromosomes or secondary sex characteristics or ovaries vs testes.
How people perceive themselves is complex, yes. But how people perceive themselves does not override reality, nor should it obligate any other person to accept their perception of themselves when it is in opposition to observable reality.
We can be compassionate, we can be caring, we can be sympathetic. We can do all of this without having to sacrifice the observable reality around us. And we can do all of this without having to sacrifice the dignity and rights of women on nothing more than the claim of some men. It is not uncaring nor cruel for women to deny access to female-only spaces to males
as a right. At our discretion, with our consent? Perhaps. But as a right based on self-declaration? No, I don't think women should be obligated to surrender our spaces and our hard-won advances to magic words. I want something more than self-declaration.