He could be "non-binary" if they wanted but we might suspect they had a political agenda, if it was introduced today.
For the vast majority of Who, all the evidence was that time lords remained the same sex when regenerating, which is surely as reasonable a bit of writing as any other, given that it's made up.
They only introduced the idea that they regenerated across sex when it became important to them to signal that they believed that sex is mutable and changeable. And that's not because they believe it is the case with Time Lords - it's because they believe it's the case with people.
They started with other characters to introduce the idea, but the moment they showed a cross-sex Time Lord regeneration it was clear they intended to have the doctor regenerate into a woman (along with other the other identity characteristics they think are important.)
It reminds me a little of the Christian heresy which said that Jesus had no sex, which I suppose goes along with the increasing sense of the Doctor as some kind of messiah figure.
But people who don't like it aren't necessarily being sexists, they may just not like the writers using a show they loved to push their own political stupid hobby horses.