The intersex athletes support this claim because, although their condition is "natural" in your sense, they are in fact being banned from participation in women's sports. For example, the various individuals mentioned above are restricted from participating in distances from 400m to a mile, including in particular 800m! (Thus they have switched to other distances, but the bans are likely to extend there too.)
Let's be honest, that's what most of these bills are marketing themselves on.
The single biggest genetic difference among humans is the presence of a Y chromosome.
This single casual factor, not "testosterone levels" nor "height" nor "bone density" nor "muscle mass", is the best factor to split on.
Accordingly, the women's division at the Olympics should be based on this factor.
(There are potentially still edge cases, but neither trans people nor even the "46X,Y DSD" individuals mentioned above are the edge cases.)
That is actually incorrect. You can be born with a Y chromosome and zero functional testosterone[1]. There are a lot of moving parts in between having a Y chromosome and getting testosterone expression. The later of which is a much better discriminator.
And also, these deviations aren't rare. Though they are usually unknown, when they don't cause obvious developmental deviation (and thus labeled DSDs). They also are more common in some populations.
[1]: https://en.wikipedia.org/wiki/Complete_androgen_insensitivit...
The silver medalist in the 200m race at the 2020 Olympics (who also holds the U20 WR for the 200m) has a Y chomosome. https://en.wikipedia.org/wiki/Christine_Mboma
(These participants are "intersex", rather than "trans".)