As pps have said though, Alpha, we are talking here about children.
It is well documented that a very high percentage of children with gender dysphoria, would resolve their dysphoria after going through puberty, and many would grow up to be gay or lesbian.
It is also well understood, that identity is fluid and still forming during childhood and adolescence (and I would say, throughout life).
Those of us who resist the move to socially and medically transition children and young people who have not gone through full development (and we have also read and listened to the stories of young detransitioners), believe it is too risky and unethical to lock children into what is statistically, most likely to be, a temporary identification crisis or period of natural experimentation. The consequences of which being lifelong dependence on medicalisation and worsening of mental health.
If gender identity is 'a fact about a person' (which suggests immutability), as you say, how does this square with the notion of gender fluidity; with the many who move frequently between different gender identities, or who desist, or who identify as both or no genders, or both at different times?
Also, there seems to be many contradictions around gender dysphoria and gender identity.
These days, people who advocate for transition, seem to be saying that it is only about gender identity, and that gender dysphoria is not requisite (and is considered stigmatising as a mental health condition.
As you seem to use both terms interchageably, can you explain what for you is the difference/relationship between gender dysphoria ( where you indicate mental distress), and gender identity (indicating an immutable fact of being)?
Many people transition later in life, and perhaps it is like this for you(?), wish that transition had been an option for them when young.
I fully acknowledge there are some (paricularly males) who will choose to medically transition as an adult, and may, yes, struggle with not 'fully passing' in the way they thought they would if puberty suppression had been available to them.
But as I see it though, life is imperfect for all of us, and there is a balance of risks and needs, both for the individual and for the group.
This why leaders, judges, and parents, and professionals etc need to be both wise and compassionate-recognising the lesser of evils, balancing risks, and being willing to upset or restrict people, but coming from a place of genuine care and responsibility.
You grew up and your gender dysphoria persisted, and as an adult, have made a choice about how to manage this. (You also say they is your fixed identity).
Others with childhood gender dysphoria grow up grateful for having not transitioned and no longer suffer with gender dysphoria.
Still others have transitioned late in life, or young, and may not regret this ever, or, may later in life come to regret this as their sense of self and identity continues to change over the course of life. Or, because of the realisation of what the childhood gender dysphoria actually meant for them, which is only recognised after life experience and deep reflection.
A growing number transitioned young and come to regret this very quickly.
I have listened to people with the full ranges of these experiences.
My conclusion is, that with such a diversity of causes, and unpredictability of outcomes, the only reasonable approach is to explore and inform fully, support with current distress, and to hold off on any any interventions that lock someone into a fixed identity and permanent physical changes until someone has reached maturity.
Adults can make decisions that they may, or may not, ultimately regret. And in fact, many adults currently make the decision to not medically transition (whilst advocating child medicalisation)- to simply 'identify as'- or only after having had the full experience of an adult sex life, and parenting for example. In other words, they have been able to fully explore their identity and their sexed bodies, and be informed through life experience and adult knowledge)
How can we ever say this is translatable to still developing children and young people?
As a society, the adults are responsible for the protection and wellbeing of children and young people. I just can't get my head around people not recognising the abdication of this responsibility.