I would go by the metric of "anyone who registers as THIS gender and has done so sufficiently in advance of the competition and has not competed as THAT gender in a specific window of time before the competition".

Because living as a different gender than other parts of society say you are is not something people do at the drop of a hat and it's ridiculous to treat trans athletes' inclusion as a slippery slope that means women's medals and prizes are gonna get stolen by men who couldn't win in their own category.

I don't know how to sensibly and fairly deal with nonbinary folks. Someone else can figure that out.