The notion that young kids necessarily have a completely formed and stabilized "gender identity" (which is necessary for "trans kids" to even be a meaningful concept) is entirely driven by ideology. It doesn't even pass the most cursory test of plausibility.
Of course it's not necessary for gender identity to be "completely formed and stabilized" to be able to talk about it. Do you think it's meaningless to describe a child as "short" or "tall" because their body is still growing?
Sorry, I don't really get the relevance of that objection.
In everyday life, most of us are happy to accept the "reality" (in whatever philosophical sense you choose to use) of all sorts of personality traits that exist only "in the mind": kindness, eloquence, sense of humor, willpower. If you likewise accept the reality of "gender identity" as a mental trait, then I don't understand why it makes sense to insist that trait is only meaningful when it's "fully formed" -- can we say that about any aspect of our personality?
I don't know if this exact question has ever been scientifically studied, but it seems pretty clear that if you offered people the choice to push a magic button and permanently change their body to the opposite sex, the vast majority of us would pretty confidently say, no, and a small minority of people would be equally confident in answering the opposite way. That's close enough to "objectively measurable" for me.
More to the point, we're talking about children. Should children be allowed to press the magic button?
We don't allow children to make other permanent changes to their bodies in general (and those tend to be stigmatized even with parental consent); and more to GP's point, the majority of children with a desire to be the opposite sex grow out of it.
It does not make sense to me that we question a child's judgment in all other matters except this one. This is important because gender affirming therapy is, medically speaking, nontrivial and not without severe risks.
