"And I would also say that someone’s internal sense of gender identity is a different thing to socially constructed gender."

You're doing the same thing the author is: collapsing sex and gender performance. Also, the claim above is tantamount to a religious claim. "Internal sense of gender" to my ears is an incoherent claim to make. An essentialist claim, in fact. And you have every right to that claim. But other's will come to a very different conclusion.