This school is a terrible idea.
Segregation and division is what we've been fighting against, not for.
Schools and centres for children and young people who have been victims of bullying to such an extent as they cannot re-enter mainstream school, whatever the motive for this bullying, already exist. This provision needs to be developed further. Safe spaces and youth groups for LGBT+ young people also already exist and must be further developed. These are good things.
However segregating young people and their educational needs, based only on sexuality or gender identity, is a bad idea. It suggests LGBT+ people are fundamentally different in ways other than just sexuality/gender.
Also, those who would likely benefit most with extra support with their LGBT+ identity are not those who would likely attend this school. Those with parents/families who reject their identity and receive no moral or emotional support at home, are not likely to have parents or families who would enrol them at such a school. Also, those who are victims of homophobic bullying in their communities are only likely to see an escalation of these problems.
Also, shall we segregate all services in order to be able to focus on the issues affecting the LGBT+ community? Shall we have queer hospitals? Prisons? Libraries? Leisure centres? If not, why not, why are these different to LGBT+ schools? Or should we have divided and segregated services and communities.
Finally, to believe that bullying would not exist at this school is naïve. Discrimination exists within the LGBT+ community already towards certain labels, bisexuality for example, or trans individuals. Also, bullying would still take place, perhaps not to such a great extent due to a persons sexuality or gender, but due to other reasons; class, weight, ethnicity, etc.
Terrible, terrible idea.