@DocStrangelove
It is conversion therapy if the therapist has a pre-determined outcome they are seeking, whether it is that sexuality must always be heterosexual or that transgender individuals do not/should not exist. Exploratory therapy allows the patient to guide the process.
I see your point to a degree. The mum (and presumably the therapist she selected the second time) had a pre-deterimed outcome in mind that they would help the daughter understand and accept her body. Similar to how someone would approach other body dysmorphia/dysphoria issues like anorexia.
I also agree with you that this shouldn't be an echo chamber. It's about listening to each other and challenging other opinions respectfully. Then listening some more and so on.
I guess the key things for me would be that no child should be making decisions about modifying their body in an irreversible way.
As I understand it, where gender dysphoria seems to branch away from other body dysmorphia is that on rare occasions, people (adults whose brains have developed past adolescence) may find that talking therapy does not address the gender dysphoria. After much consideration of the risks, the answer could then be surgical intervention. As I understand it, this is closer to the origins of gender identity care. What's happened in the last 10/15 years seems to be more of a social contagion which is impacting confused adolescent girls by providing what is effectively the wrong answer.