With regards to bullying in secondary schools - there were three openly LGBT+ kids in my school. One, the gay guy, got on alright. The two girls who started dating were bullied mercilessly and constantly for three years. It meant me and my girlfriend couldn't come out, my friends couldn't come out. It wasn't worth it. We all hid ourselves through secondary school and it wasn't the most enjoyable experience. I help run the GSA at college now, and it's not exactly uncommon experience for everyone to have hated secondary school. Whether it's worse than other types of bullying, I wouldn't know, but it's definitely bad and secondary schools rarely have an resources to counter it.
But, LGBT+ schools sound like a really, really terrible idea.
Firstly, yeah, discrimination is not going to help and you have just been outed to every future employer ever. Segregation does not solve the problem at all. It's a terrible solution, there will still be millions of queer kids in non-LGBT schools having to put up with homophobic and transphobic bullying. I'd also make the point that the article seems very focused on homophobic bullying, when lets be real, trans kids have it just as bad if not far worse at secondary school, especially if they even considered transitioning whilst there. There's a reason every trans kid I know started transition in the summer between secondary school and college, or at college.
I'd prefer integration into society than segregation from it, personally. That doesn't mean not challenging the status quo a bit, but seperatism has never been a very appealing ideology.
What is an idea I prefer, and I've seen in some American universities, is offering a 'rainbow floor' in some accomodation blocks for LGBT+ people. If you've got a big enough university, fostering community and allowing a lot of people, especially trans people, to live in a safer environment sounds like a good idea to me. Of course, universities here don't tend to have much of a problem, but I'm sure at least some of us get paired with homo/trans/etcphobic tossers in first year.