on edit: I guess from what I read there it seems he's saying being male and female are biological categories, but he does not specify what kind of category transexuality would fall under, that is to say from looking at just that page not sure if he has said transexuality does not exist, only that it must be something different than the male and female categories. Which from what he writes seems that he wants these terms to mean 'born with male organs' and 'born with female organs' respectively.
It's the same principle for most gender critical people. In this case, Wright is both a biologist and an atheist, so he's rather predisposed to being sceptical of ideologies that aren't based in material reality, given his background.
Hate speech would be an incitement to violence, or saying awful, dehumanising things about people with a shared group characteristic.
Merely exprsssing a point of view on sex versus gender identity isn't hate speech by any reasonable definition.
And sex is also widely considered a protected characteristic - by the same logic, when trans rights activists assert their belief in the primacy of gender identity over sex, are they also committing an act of hate speech?