Problems I see:
This group is arbitrarily constituted and does not share a protected characteristic. Sexual orientation and gender reassignment are different. Q means nothing in law. Allies ditto.
IANAL, so maybe
Lesbians are not underrepresented in sport generally, the opposite is true if anything. We don't know what the sport is, but if other sports are a guide, there will be no shortage of lesbians.
Since a bare 0.5% of the English and Welsh population claim some sort of identity, I think it's unlikely that the T demographic actually is underrepresented. But before we can assess whether T are under-represented we would have to know what "trans" means. Nobody seems to.
Never mind not wanting to out themselves as gender-questioning, some kids may not want to out themselves as homosexual.
There is no provision for straight or gc kids of any sexual orientation to participate. Agree with pp that we shouldn't be focusing on sexual orientation and identity anyway, at least not until they are 16.
Since it is a mixed sex sport, the T demographic don't have to take part in a team labelled one sex or the other, so there would be no reason to exclude the other kids.
The L, G or B children are as likely to experience homophobic bullying in an LGBTQ group as they are anywhere else.
Agree with the points raised by the OP at 12:50.
On the face of it, this looks like a special club set up to exclude pupils as young as 11 on the grounds of their beliefs and sexual orientation. This is unfair and also ridiculous for a school. They're just kids, fgs. It would be more honest to call it a sport club for gender zealots. It's a very bad example to set as it excludes for illegitimate reasons.
Separate point:
Speaking generally to those saying that an open category in addition to the male and female categories are the way forward, please think again. All you are doing is creating another category for men to excel in. And it would not keep the male
people out of the female category, either - the only thing that keeps the female category female is a prohibition on all males. The existence of another, mixed-sex option is as attractive to males claiming to be women/girls as the existence of third spaces generally. Not validating or exciting enough.