I looked up that barmy-sounding quote in the CofE schools guidance document Valuing all God's Children. The document is 50 pages long, mostly focused on bullying and doesn't give a lot of guidance on practical decisions like 'which loo'.
The quote:
"The protected characteristic of gender reassignment only works one way – not being transgender is not a protected characteristic. Consequently schools can make adjustments to meet the needs of a trans pupil without being accused of discriminating against non-trans pupils"
As a pp pointed out this isn't wrong: the PC of disability works in the same way. However the next thing to point out ought to be that of course schools ARE under the Public Sector Equality Duty to foster good relations between people with a protected characteristic and those without, and crucially, other people have other protected characteristics which also have to be taken into account. This is absent.
The quote is referenced to The Intercom Trust, Schools Transgender Guidance (2015), p. 12.
There's no sign of this document on the Intercom Trust website. However, this looks to be the same document, adopted at some point by Torbay safeguarding board.
This document draws the parallel with disability, and goes on to reference the PSED, though it doesn't draw out any implications, nor point out that 'special steps' might affect the rights of people with other protected characteristics, such as sex. (ie everyone).
"Unlike most of the protected characteristics, such as sex, race and religion, but like disability, this protection works in one direction only – not being transgendered is not a protected characteristic. Schools are therefore free to take special steps to meet the needs of Trans pupils without being accused of discriminating against pupils who are not Trans."
Interestingly, the Intercom Trust guidance is much less crazy than some later school 'trans toolkits' from advocacy organisations eg acknowledging some of the challenges of including boys in girls' sport rather than just suggesting that anyone who objects must be sent for reeducation or excluded.
I think schools have been desperate for guidance, and people with an agenda of 'trans inclusion is the most important thing in the whole world' have stepped into the void. The results are an appalling mess, as this dreadful story illustrates. Those poor children, all of them, but particularly the girls.