Then you should modify what you wrote. No parent has an absolute right to protect their children any way they see fit. With that out of the way, I'm sure I could come up with psychological harm cases as well--there are cases of parents making their children apparently schizophrenic in families with no previous history of schizophrenia for instance, by simply holding them to an impossible standard. For example, a mother tells her child "if you love me, you'll go get me some ice cream from the store down the street," but when the child comes back with the ice cream, the mother yells at him that if he had loved her, he would have never left her alone. And so on, day in, day out, and by the time that child is 18, he's a complete basket case.
The problem with your view is that we have to walk a fine line in judging just what does harm to children. My view is that a child who is raised to think of homosexuality as inherently wrong is harmed since that is a kind of ethical add-on to scripture that doesn't really say as much, and furthermore, it is simply the case that the world is full of gay people, and everyone has to figure out how to get along. That's awfully difficult to do when you think that something so basic to another person's psyche as their sexuality is inherently morally wrong. I've never met a human being who could pull off the feat of loving the sinner but hating the sin. The few genuine Christians I've ever met who really did figure out how to love everyone were at best saddened by human wrong doing; hate was not anywhere in their character.
I think the question of whether the state has a right over the child that is greater than that of the parent, or vice versa, is based on a flawed assumption. The child is a human being, and no one, not the parents, not the state, no one owns the child. We have to start there, I think, and that means that neither state nor parents may indoctrinate children.