A pride flag is a symbol of acceptance. It's saying that it's okay to be gay. It's not saying you have to be gay, it's not saying you have to like that people are gay, just that it's okay to be gay.
Well, in the same way you could say that the Ten Commandments are just a symbol of respect. You don't have to like them, you don't even have to follow them, but it would be nicer if you did.
The first one is not authoritarian. Not giving orders to anybody, and not restricting people outside the group that created it.
Try seeing what happens when someone dares to remove the flag, or even just says in its presence that they don't like gay people. I bet you the authoritarianism is going to show up real quick.
I've seen enough evidence to be convinced that it absolutely IS happening.
Yes, there is no government mandate to do that, but it is happening nevertheless. There are tons of videos on YouTube of teachers explaining why it's important to them. And while it's true that LGBT doesn't meet the definition of a traditional, organized religion, it does strike me as having quasi-religious character, as evidenced by the automatic assumption that anyone speaking out against it is acting in bad faith (i.e. committing blasphemy).