The vast majority of people with some kind of intersex disorder are still very clearly either male or female. Hermaphrodites, that is, people whose primary sex organs developed in a way that make them truly ambiguous, are vanishingly rare. And in that case it would be acceptable for them to identify as whatever sex they feel is the closest.
My problem is not that I'm never willing to be generous and charitable with people who are genuinely edge cases. My problem is corporate and government policies that require me to lie about non-edge cases.
* I know a lot of trans people - MTF and FTM - who are not distinguishable from your definition unless you interrogate their genitalia, or in some cases, their genetics. If you see such a person, and use the "wrong" pronouns according to your definition for them, would you then feel guilty for not using the "right" ones? If not, why not?*
Again, my problem is required being to lie. If I have a coworker who I know is a man, he has always called himself a man, he has the secondary sexual characteristics of a man, he is six foot with a beard, he has sired a child -- and then one day he comes into the office wearing a dress and long-hair and insist on being called a "she" and insist on going into the woman's locker room at the gym, I would find that intolerable because I know the coworker is not a woman. I am being told to lie.
If my boss says "There are four marbles in this box" and I have never seen inside the box, I will say, "Ok, got it, I have no reason to accuse you of lying, there are four marbles in the box." But if I see with my own eyes that there are two marbles in the box, and my boss says, "There are four marbles in the box, say it say 'there are four marbles' it or you are fired" that is dystopian and intolerable.
Now, let's say I have a coworker who always presented as female, the coworker maybe had a bit of an uncanny valley thing at times, but I have never asked about it and have always called the coworker "she." One day, there is a work-family outing to a water park, and in the locker room the coworker is naked and exposes zis penis in view of my wife and daughter and they tell me about it. I would not feel guilty about calling the coworker "she" but I would feel angry with the coworker for lying about his sex.
And even if that isn't true, why does "adult human female" have to map to "woman", and vice versa?
The entire point of language is to "cut reality at the joints", we create words in order to group natural kinds together in a way that allow for common understanding and decision-making. If society wants to redefine "woman" as meaning something else, we would still want a word to mean "adult human female" because it is a natural kind. When we redefine woman, we see all the contortions people go . All of science, all of human knowledge relies on being better and better at organizing and recognizing and create common language around finding patterns in nature.
All of this is to say that I don't see how your reduce-it-to-biology-and-never-waver definition is workable in society, and I don't understand why folks - yourself included, it seems - are so insistent on it.
For all the reasons we make distinctions between men and women, or divide up men and women -- from locker rooms to sports to prisons, to assigning rooms during multi-family vacations, or assigning rooms at college, to single-sex schools, to certain dress standards, to sexual harassment litigation, to etiquette and social norms around inviting people to do activities -- it all comes down to biology. It all comes down to massive physical disparities between men and women (eg, a punch from an average man does to a woman does approximately 1000% the damage a punch from a woman does to a man), and the male potentiality to impregnate women, and all the physical and biological differences that have evolved as a result of reality. The reason historically cultures have clothing and appearance cues to distinguish sex is because the biology is very important, we want to know it as soon we meet someone, but we don't want to look at their genitalia, so cultures have arbitrary conventions (pronouns, male & female names, pink versus blue) etc. to indicate biological sex at first meeting. Destroying these distinctions and saying, "it's all what a person wants to be" is completely novel in history and the burden of proof is on those who want to change the status quo, and after following this issue for 15 years I only become more convinced that burden-of-proof has not been met and that it really does all come down to biology.