I disagree with quite a lot of this.
First of all, and I realise this opinion isn't shared by everyone, I am wholly unconvinced that LGBTQ+ is an underrepresented or discriminated against group. LGB certainly was historically an underrepresented and discriminated against group, and still is in certain ways. The TQ+ only really hitched themselves to the bandwagon once the LGB had already made huge amounts of progress.
In terms of representation, we have Pride Month, where every major town will have Pride events and essentially all major workplaces will celebrate Pride in some fashion. I am a lawyer, as it happens, and I can tell you that during Pride month my entire LinkedIn feed is awash with rainbows as all the firms I have ever worked for and all the firms my contacts work at change their logos to have a Pride flag background. Huge amounts of public discourse are taken up with talking about the rights of trans and non binary people. I would argue that no other identifiable group has this much representation.
In terms of discrimination, no other group is allowed to use toilets or changing rooms, join support groups or compete in sports for members of the opposite sex. No other group is allowed to dictate how others refer to them and how others are referred to. No other group has succeeded in getting so much of their own personal belief system to form the basis of public policy. No other group has managed to get people fired from their jobs for not sharing their belief system, or have all single sex support for female rape victims made mixed sex to include them.
So no, TQ+ are not what I would call an underrepresented or discriminated against group.
Secondly, you are conflating LGB with LGBTQ+.
LGB is, as I mentioned above, still an underrepresented and discriminated against group. A very obvious example is that when some of them set up an LGB charity, they were taken to court for setting up a charity of their own which did not include TQ+. During those court proceedings, the chairman of the LGBT+ consortium, a group which represents over 300 LGBT+ charities in the UK confirmed that their collective position is that gay and lesbian are now words for people who are attracted to people who share the same gender identity as them, and that anyone who believes, as LGB Alliance do, that being gay or lesbian means being exclusively sexually attracted to people of the same biological sex, is transphobic and not welcome in their organisation, and should not be allowed to exist.
So I would agree, based on the fact that that was allowed to happen in open court, that LGB is an underrepresented and discriminated against group. It is also an identifiable group sharing a single protected characteristic which, as you quite rightly state, should be allowed to have its own groups and this is confirmed by the Equality Act, even if the LGBT+ Consortium disagrees.
But this ping pong club is not for LGB students. It is for LGBTQ+ students and their allies.
That means it is for gay students, lesbian students, bisexual students, students of any sexual orientation with a transgender identity, students who identify as queer I don't actually know what this means but I know that some gay people consider it an offensive slur, students who identify as something covered by the + again I have no idea what this means but I know the LGB Alliance have some major concerns about what might be included here, and straight students who consider themselves "allies" of these groups.
This is not an identifiable group sharing a protected characteristic with a legitimate need to have its own groups from which all others can be excluded.
This is a group which includes potentially everyone, except students who are not "allies". And as many of us have already pointed out, the only thing this can possibly mean is students with gender critical beliefs. So it is a group which is open to everyone except a particular group of students who hold a perfectly legitimate belief that those who have formed this group happen to disagree with.