WoT happens in a medieval/Renaissance-like setting, where there is no gender-reassignment therapy nor psychiatrics. In such a world contemporary trans-people would grow up as gay or lesbian or plain cisgendered or repressed. Whatever they be, it won't be acknowledged as trans.

Of course you could say even if people are not identified by a licensed psychiatrist, they still may have gender-dysphoria, and it is only societal pressures who force them to adopt an assumed identity.

But maybe the ingrained assumed identity is enough to direct the connection to the one power ?

If not, and we assume only the contemporary true-to-self identity matters, then what about non-binary individuals ?

They tap both halves ? But that's over-powered.
They tap none ? Makes them crippled.
Randomly tap just one of them ? Denies their identity.

IMHO it breaks the magic system.

As a compromise, you could have the Forsaken say something about how in the Age of Legends gender-reassignment using the One Power was a thing. Maybe change it so Balthamel is Aran'gar from the get go, and doesn't die in the Eye. That way you can also preserve the Egwene headaches plotline.

Yes, I think this is good. I can envision the Red Ajah gentling men who can tap Saidar as an extra-fuck you to penises.