I did read it. You are saying that it's about whether someone claiming to be of a specific gender is enough to make that person that gender, which is an odd question. Someone else is saying it's about the locker-rooms. That's why I'm confused.
As to your specific problem, the answer is both yes and no. It's enough for that person, and any person interacting with that person on a casual level. Or at least it should be. The thing is, we're not talking about just "claiming" to be a specific gender. We are talking about a mindset, a personality and quite often medical procedures.
So since I'm the one who brought up locker rooms, I'll chime in.
The locker room is a concrete example of a more general situation. The question is about whether someone feeling like/identifying as a particular gender actually made him that gender. Is a biological male who identifies as female, really female?*
That's a rather abstract question. We can debate if this fellow who just gave birth is "really" a man or not. Our answer will not have any real significance all by itself. He/she will be exactly the same person, regardless of whether we call him/her a woman or a man. (To refer to an oft-quoted story, usually attributed to Abraham Lincoln, if we call a tail a leg, a dog still has four legs, because calling a tail a leg does not make it a leg.)
The question becomes more concrete, though, when, we take it out of the abstract theater, and realize that in addition to a hypothetical question about someone's true nature, we realize that what is being asked is that society should change its behavior toward that person. What is being asked is that the rest of us, all who interact with a transgender person, ought to do something different.
Now that becomes more concrete, and different people have different thresholds of exactly what they are willing to do in order to go along with the belief that the transgender is "really" the sex they identify with. For example, we are expected to use gendered pronouns to refer to their preferred gender, rather than their biological identity. That's a rather small thing. Some people refuse, as a matter of principle, or out of a fear of a slippery slope effect, but most people wouldn't be bothered to put up a fuss. On the other hand, there are situations where we, in our society, have occasion to be naked or seen in our underwear by strangers. In those cases, we try to restrict the sex of those strangers to be the same sex as ourselves, and in the modern world, we are being asked o view the sex of the transgender as their preferred sex, rather than their anatomical one. That's a line that an awful lot of people would prefer not to cross.
To put it more bluntly, if you want to be called "Ma'am", when you are ordering coffee at Starbucks, fine, but if you have a penis, stay out of the girls' locker room. More generally, in situations where there are no consequences to treating someone as a man or a woman, we are willing to go along with the preferred gender. However, in situations where we really care whether we are dealing with a woman or a man, and we would behave differently depending on the gender, we might insist on using biology as the criterion for deciding who is what.
*I've decided that for this post, I'm going to use the terms "sex" and "gender" the way they would have been used 10 years ago, when they were considered interchangeable synonyms. The distinction was a linguistic device created in small part to help distinguish between self identification versus biology, but in large part as a way of advancing an agenda and making some people feel much smarter because they could "correct" other people about their language use.
