I, too, feel sorry for the kid--but your analysis has glossed over a few distinctions, the most important of which is that the school is NOT condemning, nor punishing, the child for the 'sins of her parents.' Rather, they simply denied admittance.
The child will have a fine education at the local public school. She has not been denied an education, nor has she gained a red-letter LESBIAN CHILD tattoo on her forehead.
See my post above for the other practical problem her admittance would bring.