> Everyone — even rare intersex individuals — can only belong to one reproduction class or the other.

In principle, this is not necessarily true in Ovotesticular DSD (formerly “True Hermaphroditism”), which is generally a symptom of tetragametic chimerism, though for both health and gender reasons it is apparently not uncommon for people who naturally have both functional ovarian and testicular tissue to have hormone therapy and/or surgery to align more with the sex traits stereotypical of a single preferred gender.