Fixing an Unfortunate Implication: Non-Cis People in The Wheel of Time

[Mechalich]

Aran'gar disproves that, though... or rather, is the only evidence one way or the other, and is not in favor of that interpretation. As the only trans person we see in the setting, he is a man in a female body, and has access to Sai'din.

Like I said, at least half of fixing the problem is as simple as making Aran'gar either channel Sai'dar now or be shown/told to be an exception to the rule. Then voila; the textual evidence (or I guess visual evidence for a show? Scriptual evidence?) is now in favor of channeling being determined by sex instead of gender, which like you said is perfectly consistent with every bit of evidence except for Aran'gar.

Insofar as Aran'gar has a function in the story, it's as a physically female body capable of channeling Saidin, because that enables Aran'gar's infiltration of Salidar, which is basically the entire post-reincarnation purpose of the character.

And there is other textual evidence for gender fixation of the soul in the setting anyway. In particular, when Rand takes the portal stone journey during The Great Hunt he lives through something like 100 lives and he's male in all of them. Similarly, when Rand travels to Rhiudean and lives through the history of the Aiel, he always takes the viewpoint of a male individual, never a female one, while when Aviendha journeys into the future in the same place all of her viewpoint descendants are female. All in all characters jump into the memories of other characters dozens of times throughout the series, but unless I'm mistaken no one ever spends time in the viewpoint of the opposite gender.

Aran'gar was created by the act of an evil deity who can break whatever rules of the setting they want. Calling them trans is also questionable in the first place.

Indeed, especially because the Dark One messed with mind as well as body and overwrote Aran'gar's memories so that she became female in the hundreds of years worth of life that had been lived as the male Eval Ramman. Not sure what to call that but it's not comparable to any real world trans scenario.

The existing evidence suggests that souls pledged to the Dark One are functioning under a different set of rules than those of normal people with regard to how reincarnation works in WoT. Normally people go round-and-round the Wheel, but those whose souls belong to the Dark One are his to do with as he wills, including the ability to remove them from the cycle forever if he wants - it is strongly implied that this is what happened to Asmodean when he was killed.

Ultimately, there's lots of weird stuff about souls in the WoT, including the ability of mortal channelers to destroy immortal souls using Balefire, which is just theologically bizarre. So really you just have to roll with it.