'Oh what a tangled web we weave/When first we practice to deceive'
You may not find the magic bullet quote, Drain and instead have to walk the school through the process of how we got to this point. Maybe the best you can do is to get the school to think 'minefield' rather than waltzing into it unthinkingly.
According to the style guide sultana posted, the NHS website makes a special concession when talking about 'sex' to an audience who is looking for information about gender identity and dysphoria, that it will not use elsewhere, eg when talking about sex-specific cancers.
Why they make this linguistic concession and who encouraged them to make it would be very interesting to discover. I would put good money on it being GIRES and/or Stonewall because it is definitely not medical or scientific or actual reality based thinking. I wonder if it is FOIable?
It uses activist language like 'assigned' to appease a group which has not only tried to rewrite the meanings of 'male', 'female', 'men' and 'women', the most fundamental building blocks of society, but also co-opted the language of the intersex community to do so.
"We use the phrase "sex assigned at birth" when we're talking about trans health and gender dysphoria, as this is the language our audience uses.
It reminds me very much of Helen Joyce saying about gender ideology trying to make 0=1 and people not seeing the potential knock on consequences if they give ground in just one area. It's the 'genderist tail wagging the medical dog' territory.
In other cases, we use "the sex someone was registered with at birth" because user research shows that most people understand this better as it refers to an actual event.
I feel your frustration because when my oldest suddenly began to identify as trans a few years ago, they pointed to the NHS page on gender dysphoria, then with assertions such as puberty blockers being reversible, as if it were gospel truth.
A family member is a psychiatrist so was able to challenge it from a medical and scientific point of view but they have found their Royal College to be equally captured, using the activist language and pathologically resistant to change.
I just think it makes the RCPsych look really scientifically dim when they talk in their position statement about being 'assigned' anything at birth.
If it is hard for adults to get to grips with, what chance 10 year olds...