While you're right that there's no connection between being trans and being intersex (except that intersex people are probably more likely to be misgendered at birth), it's not the case that intersex people are 'extremely rare'. Depending on definition, we are talking about ~1% of people. For comparison, that is e.g. around the percentage of men who are 6'4 or taller (in the US).
This is not an endorsement of any particular take in the thread, but this seemed like an appropriate place to correct a mistake regarding the frequency of intersex births and link out to some articles for the curious.
That 1% number comes from the Fausto-Sterling survey which incorrectly lumps in Klinefelter syndrome, Turner syndrome, and late-onset adrenal hyperplasia. Eliminating those diseases yields a rate no higher than 0.018%, 2 orders of magnitude lower as the upper bound[1]. Only a small portion have cells for producing both types of gametes, only about 5% of all intersex people[2][3].
The controversy about what counts as 'intersex' is mostly pointless, as far as I can tell, as the term neither has (nor requires) a precise definition. I think in this context it makes sense to include any condition that blurs the edges of the gender binary as traditionally understood in society. If you look at the details of e.g. Klinefelter syndrome from this perspective, it's not difficult to see why it might be seen as part of the intersex spectrum:
>broad hips, poor muscle tone and slower than usual muscle growth, reduced facial and body hair that starts growing later than usual, a small penis and testicles, and enlarged breasts (gynaecomastia)
It's by no means a settled matter what does or doesn't count as 'intersex'. I suspect that few reputable researchers would waste time engaging in such a pointless debate over terminology. Some relevant points in this article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5808814/
All that said, one can, if one wishes, cherry pick the smallest available estimate of the number of 'intersex' people and thereby dismiss the issues raised by these people on the grounds that they're small in number. I'm not sure how much scrutiny the logic of that rhetorical move would withstand.
I’m not trying to make any claims about the broader issue or cherry-pick here, but a lot of experts do not include Klinefelter syndrome so I think that’s worth at least noting. Moreover I think pointing out that 95% of the people in question clearly have cells to produce a single type of gamete and are often fertile is instructive.
My only point in responding is to add useful scientific/medical context. People can make what they want of that information.
Fundamentally I agree with what you seem to be getting at, taxonomy is hard.
> Moreover I think pointing out that 95% of the people in question clearly have cells to produce a single type of gamete AND ARE OFTEN FERTILE is instructive.
It’s only informative if it’s true. With regard to the second conjunct, people with Klinefelter syndrome and Turner syndrome are typically functionally infertile.
I’m not convinced that ‘a lot of experts’ are even working on defining what counts as ‘interesex’. It would make more sense to listen to intersex people, who as far as I can see, tend to think that a fairly broad definition is useful.