I would point out that Stonewall is in legal and financial difficulties, largely due to its own mismanagement.
They have been found to have given incorrect legal advice by either deliberately or negligently misrepresenting the law when delivering training to employers, particularly regarding single sex spaces. This is an incredibly live issue in the wake of the Supreme Court judgment. Over the last few years increasing numbers of employers have been cutting ties with Stonewall and that trend is likely to continue and even accelerate now.
They have also come out with some pretty homophobic statements such as calling lesbians prejudiced for not wanting to have sexual relationships with trans women. This has led many people to question whether Stonewall actually support the rights of same sex attracted people anymore, or whether they have become solely a trans activist organisation.
By publicly supporting Stonewall the school is taking a political position in favour of a highly controversial organisation.
It's also unclear what supporting Stonewall does to help children who are struggling with their sexual orientation or gender identity, and children should really be the school's focus.
The difficulty is that I can't think of a charity to suggest instead of Stonewall.
Ideally something focused on children, but not one which is going to encourage them to transition, like Mermaids. Perhaps a charity focused on advocating for gay people's rights in developing countries.