Maybe reframe this?
Due in part to the length of the waiting lists for child gender identity clinics in the UK, the overwhelming majority of kids in schools who identify as trans have never seen a gender specialist but have effectively diagnosed themselves with gender dysphoria.
Medical evidence and the historical dearth of trans teenagers in British schools over many previous decades shows us that without social/medical intervention, in the vast majority of cases up to 95+% of children with dysphoria desisted from a trans identity on going through puberty, many later describing themselves simply as gay or lesbian.
Whereas almost 100% of children who go on blockers proceed to cross sex hormones.
The latter group will be medical patients for the rest of their life, with increased risks of strokes, heart attack, suicide, cancer, osteoporosis, difficult surgeries, early menopause, dementia, sterility, shortened life span etc.
The Tavistock data shows that this is a vulnerable group with significant comorbidities - 25% ADHD, 30-60% Autism, high rates of Eating Disorders, Anxiety, Depression, Abuse, Adoption, OCD, bullying etc.
Transition cannot change this background so a child with gender identity issues will still have to deal with the comorbidities and even the dysphoria, sadly, may well still remain after medical and surgical input.
Schools which, quite rightly, will not administer any medicine to a child without the named box/dosage seem strangely confident about initiating and offering their own form of unevidenced 'treatment protocol' (without any medical input at all) where they are prepared to countenance, for example, that some boys are now girls, call them by a girl's name, she/her pronouns, hold a special celebration assembly, allow them potentially to use girls' spaces and PE sessions - and make it difficult for the teen's female peers to express any discomfort whatsoever because of 'inclusivity'.
What is the effect on the plasticity of the developing child's brain?
I would be tempted to reverse the question and ask the school, Where is their medical evidence underpinning the rationale and success of their chosen treatment protocol, or that recommended by the external group, without a diagnosis, bearing in mind that they are not mental health professionals?
How confident are they that what they are doing is not actually reinforcing something that a child would have naturally grown out of as in the past, when we didn't have swathes of 'trans and non-binary children' in schools, which instead potentially leads to them becoming a lifelong medical patient with the concomitant risks?
Could a person potentially sue their school for having reinforced or prolonged their dysphoria by socially transitioning them?
What might be the potential safeguarding problems when all the trusted adults in a child's life refer to a male person as a girl? Residentials? Changing rooms? Safety in PE?
How easy is it nowadays for a child to desist (having socially transitioned at school) when everyone else around them is so invested in maintaining their trans identity?
Medical doctors are not in agreement, some gender specialists are strongly against early social transition of children and yet this school knows better? How?
www.cambridge.org/core/journals/bjpsych-bulletin/article/sex-gender-and-gender-identity-a-reevaluation-of-the-evidence/76A3DC54F3BD91E8D631B93397698B1A
It's up to them to prove that their treatment protocol works and is safe, OP, not you. And if the group they refer on to can't provide the required medical evidence, then maybe that will set the school's alarm bells ringing...