How many times do I have to say this?
Using "male" and "female" - however we define those categories - to control access to "sex segregated spaces" is probably or largely the RONG tool for those jobs.
One set of toilets, change rooms, prison cells, and shelters for the vagina-havers - and reasonable facsimiles thereof - and another set for the penis-havers - and reasonable facsimiles thereof.
Women's sports is something of a proverbial edge case where the criteria should probably be - as I've said several times: no XY need apply.
Reproductive status is largely irrelevant, a red herring the size of Moby Dick.
How many times do I have to ask whether a credentialed Fellow of the Institute of Biology telling you that the definitions you can't let go of are not the definitions in use in biology and so not the "biological definitions" is something you might take on board?
There are a lot of competing proposals for who should be allowed in which ostensible sex-segregated spaces. Women do not by and large agree with your proposals, which means that while you get to propose them you do not get to talk as if these proposals are the last word on the subject.
Having or not having a vagina or a penis, or indeed a reasonable facsimile thereof, is one proposal which has been put forward. As regards places like women's lavatories, where entry is unrestricted, by the time I find out that a male person who has come in has or has not had his dick cut off, things have gone way too far in a direction I don't want them to go in at all.
The main thing women want is the ability to police our spaces so that males can be ejected. A law which allows males who have had invisible surgery the right to enter is no bloody use to us. Women use our female-only loos in ways men do not understand and I for one am tired explaining to men that their idea for solving everything is a dud because of factors they're not even aware of.
There are plenty creepy, fetishistic autgynaephilic men who have had "bottom surgery" and we don't want them in our intimate spaces any more than we want the ones who haven't. Particularly since they look exactly like creepy fetishistic autogynaephilic men who have not had "bottom surgery" and we won't find out until too late.
No XY need apply in women's sports? Why not? Who are you to tell women with Swyer's syndrome or CAIS that they can't compete in women's sports? That definition is so outdated it's a wonder to see anyone putting it forward. Maybe you'd let XX men compete? The one they seem to be going for is that nobody who has been through any part of male puberty can compete in women's events. That is a pretty good rule. (And you know what? Who are the people who will never go through male puberty? Funnily enough, the people who do not have a functional SRY gene system (as defined above). The Venn diagram is a perfect circle.)
Reproductive status, as this is normally understood, is indeed irrelevant. Reproductive status is things like have you ever had a child, are you pregnant, are you currently cycling normally, are you amenorrhoeic (due to too much training probably), are you post-menopausal. Women come in a wide variety of reproductive statuses. Men too, though not as wide a variety. Your reproductive status is irrelevant. It's your membership of one or the other sex class which is important.
And having gone through any part of male puberty will do just fine for me. It will also do just fine for entry to toilets and so on, because we let little boys come into the Ladies so long as they're pre-puberty anyway.
People have pointed out that this allows males who were puberty-blocked before starting puberty, and then castrated, to enter women's sports. It's a non-objection, because the adverse effects of the hormones their bodies have been given is unlikely to get them any further than their first fracture. We can also let them slide in the single-sex accommodation too. They are to be pitied, genuinely, and they're not going to create trouble in women's spaces.
So, while it doesn't do a biologist's job in distinguishing between male and female children, the "has undergone any stage of male puberty" works pretty well for most practical purposes.
And if you want to know with 100% certainty who WILL go through male puberty, find out if they have a functional SRY gene and all the associated enzymes and receptors for it to be expressed normally.
