Nobody is saying LGBT groups should not exist.
This is not an LGBT group. It is a ping pong club which excludes a particular group of students on the grounds that they hold a legally protected belief.
This is not about creating a safe space free from homophobia and transphobia. (Indeed, as many posters have pointed out at length, there are aspects of gender ideology which are clearly and explicitly homophobic, such as the idea that lesbians should be open to having sexual relationships with trans women, and so for students who are lesbians and wish to play ping pong, this club is clearly not a safe space from that kind of homophobia.)
It is legitimate for a school to have an LGBTQ+ club for LGBTQ+ students to meet and connect with each other. I have no doubt that such a club exists.
It should also be legitimate for a school to have an LGB club which is only for students who are same sex attracted and does not include heterosexual students with gender identities, but sadly such clubs no longer exist and we all know the reason why.
But when it comes to sports clubs (or indeed, music ensembles, drama clubs, chess clubs and any other clubs which are for students to enjoy hobbies which do not have anything to do with their sexual orientation or gender identity), (1) all students should be equally welcome to join, and (2) the school should be operating a zero tolerance approach to any kind of bullying, thereby negating the need for specific clubs to be designated safe spaces free from any particular kind of bullying.
But this is not about providing a safe space for LGBTQ+ students to play ping pong.
It is about ostracising students with gender critical beliefs and excluding them from regular parts of school life.
Every time the apologists on this thread talk about gender critical beliefs not being a justification for discrimination, they are ignoring a crucial point. The LGBTQ+ people are not the ones being discriminated against here. They are the ones doing the discriminating.