It's fine to be gay and teach. It's not fine in schools, from the parents and admin perspective, to teach LGBTQ in school. It fits the same as religion from most people's perspectives. If you're teaching sex ed and it's time to explain that some people are different and it's necessary to know how to be safe etc, then sure.
Please note that I do care about people's feelings. I'm just staing from the perspective of people who sign your paychecks and the majority who are paying the taxes that pay those paychecks.
You can't discriminate against people for being something, but you can stop things that will cause uproar with parents and lawsuits for things considered agenda and grooming into specific ways of thinking.
The thing about literature is that typically you don't have students reading things that incorporate sexuality or sex in it in the first place....so I could see that if the story is just about a guy or girl that says she's gay and she's just talking about the plight of gay people, it would probably be ok. If it's something that talks heavily about the more personal lives of gay folks, then it's not ok.
All growing up, it was even dangerous to choose books that you didn't know had sexuality in it and you'd have to profuseley apologize. Now we live in a time that LGBTQ isn't a lifestyle, it's a political stance and a big one with an extreme impact on a lot of things. If you're just a person doing a job, it's better to keep your personal interests out of the classroom for your own sakes.