Go on chaps. Prove that gender is a better way to pick categories for sports or healthcare than sex is.
This is actually one of the places where there is a very small scrap of meat, and I think GC people tend to gloss over it.
Sport is not reproduction. Why should reproductive class matter to sport?
The answer is that, strictly speaking, it doesn't. And we see this in (good) rules handling DSDs.
Sport classification is designed to increase participation. Because of our 2-sexed reproduction system, there are 2 standard phenotypes for humans - the male and female phenotypes.
99%+ of the population have one of these 2 standard phenotypes. Hence 2 classes called "men" and "women" can include 99% of the population, giving meaningful competition to both. Without that split, 50% of the population - the female half - would be excluded - unable to ever win an event at top level, and at lower level an exceptional female athlete would be competing against average males. The 3rd XI football team in a school might have 1 female player - the best girl in the school. No other girl would get to play.
That 2-way split is necessary to include the female 50%. It still doesn't include everyone. We have further splits in some events for weight, making them accessible to more, and we have splits for handicaps, leading to the Paralympics.
When it comes to a very small minority of people with sex-related disorders, their classification may not directly align with their reproductive function. For 99% of people, their phenotype is standard for their reproductive sex, but some do have some variation.
For that very small minority, we need to decide how to classify them, making it fair both for them and for other athletes. It may or may not align with reproductive function - their overall body is what matters. (For some, like Semenya, it's mad that their classification is even controversial. Semenya is reproductively and phenotypically male, aside from some possible genital formation issues, but you don't play sport with your genitals). The IAAF DSD rules make very clear that they're not saying anything about someone's legal status, or identity, or gender. They're ruling on your "sporting sex", which may be different from other classifications.
But trans people are not part of this small minority with non-standard phenotypes. They're normal males and females who might choose to take performance-decreasing or increasing drugs. That choice is up to them, but performance-enhancing drugs rule you out of competitive sport, and performance-decreasing drugs are not a justification to be placed into a lower category. (The same logic barring general doping surely applies - incentivising people to take drugs to increase chance of winning is bad!)
It is notable that many trans-rights advocates get suddenly very rigid about binaries in this area. They won't accept queering concepts like "some men can be mothers, get over it" or "some women compete in men's sport, get over it". Labels suddenly get very important and rigid for them, when convenient. "Some men compete in women's sport, get over it" seems to be accepted though. Weird. 
Anyway, the important point is separate male+female categorisation is ALL about inclusion. THAT is the inclusive policy. One simple split includes 3-4 billion people. Undermining that split screws over 3-4 billion people.