It's a tough situation.
While the mother is certainly taking a stand for her politics, who are we to say she's opposing her child with bad will?
Can a person in their adolescence truly without error decide for themselves if they are born in the wrong body?
Should the first course of action when a child voices these speculations about themselves be an immediate regimen of HRT?
Especially in a world rife with social engineering and programming, where the more prevalent a thing is, the more likely others are to engage in it.
As someone who suffered from gender dysphoria in the past, I could see 10 years ago how absurd the community was becoming:
there is a difference between legitimately having extreme gender dysphoria to the degree that transitioning is necessary for psychological well-being, and then the people with identity crises who call themselves "demi-boys" yet want to be a girl, but want to remove their breasts, or just get on T to look like their favorite anime character or some shit.
They treat it like it's Cyberpunk 2077 and they're just modifying their avatar, not realizing the serious consequences.
So yeah, I think the woman is doing her child a favor by not immediately caving to what could possibly be a whim.