If they invite EVERYBODY in to proselytize, including atheists, agnostics, etc., then they are being quite neutral. It's the selective invitations that violate the neutrality principle.
But I quite agree with you that public schools simply shouldn't exist.
The question of "selectivity" is mere semantics. Neutrality means that even a federal judge ought to totally ignore any question that raises the question of whether words or deeds are religious in nature.