“Okay” with their existence. Not with protecting them from abuse and persecution.

I guess it depends on what kind of abuse we're talking about... but in many places I believe just the cessation of abuse and persecution from the direction of the government would be a pretty big positive change.

Or perhaps I don't have enough imagination. Can you tell me what kinds of protection LGBT people need that other people don't need?

It is why the silver bullet is, and always will be, “explain how orphanages work under libertarianism”

Can you elaborate? I don't get what this is implying.