Okay, it's a nice idea in theory, but there are several glaring problems with the concept.
Most kids don't even know that they're LGBT until their teens at the earliest. I wasn't comfortable identifying as bisexual until I was halfway through my last year at school, and didn't even tell my closest friends until the end of the last day. Not to mention that going to this school would mean that the kids needed to come out to their parents, something I'm still not comfortable with despite having a girlfriend for over six months. Children can risk their parents reacting with disbelief ("it's just a phase", "you're too young to know", "you would have known a long time ago", "I think I would know if my own child was gay", etc), anger ("no son of mine is ____") or even disowning their child. Failing that, there's the risk of parents being abusive in other ways - just look at what happened to Leelah Alcorn. The vast majority of LGBT kids don't want to be singled out - they want to be treated equally, not differently. They really don't want their identity to be a big deal, any more than they want their eye colour to be a big deal.
Also, there's the question of where to draw the line. It could be taken as literally only lesbian, gay, bisexual and transgender - but what about people who identify as pansexual? It's very similar to bisexuality but is largely ignored by the cisgender heterosexual majority. I'm assuming non-binary identities would be included as a subset of transgender, but what about asexuals? Some people say that asexuals "don't count". Then there are the people who identify as a different species (what?) or tell everyone "hi i am a dragonkin and i eat diamonds despite the fact that my digestive system can't process them because i am special oh did i mention i'm a dragon", and demand to be included in LGBT spaces and discussions. Also, there's the whole difference between sexual and romantic attraction, which I could go on about for pages. I won't, but in short, it complicates things.
That brings me nicely to my final, and probably most important, point. The people who came up with the idea for this school seem to think that it will solve the problem of bullying that LGBT children face because of their identity. Well, newsflash - there is bullying within the LGBT community. Take bisexuals, for instance. We're spurned by monosexuals (people only attracted to one gender), either by gay men and lesbians for "not being gay enough" and "just wanting to be special", or by straight people for being "untrustworthy" and "more likely to cheat". This even applies if we've been in a relationship with only one person, ever. People of all orientations are constantly telling us, "bisexuality doesn't exist so u r pansexual yes that is what u r". Even pansexuals, who you'd think might understand us a little, are always looking down on us from their high horse yelling, "BI MEANS TWO SO YOU'RE ALL BINARIST!!!!111!1!!!111!11!one", despite the fact that bisexuality is defined as attraction to two or more genders. And that's just one group out of all the other minorities.
It's a nice idea from a straight person's point of view, but this new school really won't help things.