Bottom line - your child's deeply held, sincere belief that they have a gendered soul which doesn't match their biological body is neither here nor there. I don't share that belief, but I respect their right to hold it.
What does matter are the political implications of that belief.
Is it a private belief, private to that individual, like a Catholic's belief in an immortal soul that goes to heaven, or a Buddhist's belief that they will be reincarnated?
Or is it a belief to be imposed on the rest of us, by insisting that rapists with penises should be housed in women's prisons, or that people with penises and typically male musculature should be allowed to compete in women's sport, or that women should be forbidden by law from organising single sex provision for, say, rape crisis centres?
The latter, public implications for law and women as a sex are all I care about. Not what your child believes about themself.