@hepwo you are not thinking about this from the perspective of lies, damned lies and statistics.
The ONS is a credible organisation who use a robust and published methodology. The ONS has defined what it means by GI and asked a question, which they have tested out and adjusted, with the aim of capturing the gender identity of the population of England and Wales. This is a credible methodology for collecting data, analysing it and drawing conclusions. the sample size and the fact it is part of a much larger survey adds to the credibility.
You have effectively stated the whole 2021 Census is not “scientific evidence”, dismissing its whole methodology and approach because of one question. You will never win that argument.
Consider my approach, treating the 2021 Census as scientific evidence and turn it round and use it to make our arguments. Most people won’t think about it a deeply as you are.
A good example was when I was watching one of the Scottish Government Committees about lessons learnt from the Adam Graham/Isla Bryson debacle. The Head of Scottish Prison Service was asked about transwomen in women’s prisons and if any of them have convictions for violence and/or sexual abuse. She deferred to her colleague who carefully said “not with a live conviction”. I expected someone to ask what about spent but no one did. I strongly suspect had the answers been no they would have said no. They didn’t lie they selectively used the data.
Remember one thing that TRAs, Stonewall, Mermaids, NHS, the Police, Scottish Gmt, RMW etc. agree on is they don’t want accurate data collection and analysis.
So back to the op. How would a school prove the 2021 Census results don’t mean anyone who said not applicable or chose not to answer that question can’t be interpreted as not having/believing in gender identity? They can’t argue the wrong question was asked, they can’t say there isn’t a definition of GI etc. any dispute undermines their own position.
So you can believe the question was wrong, you can believe the data/stats are fundamentally flawed but don’t dismiss using them to illustrate the flaws in the GI position.