I'd side with the Amish. My problem with Douglas's reasoning, and yous, is that you treat 13-14 year olds as if they are emotionally mature enough to defy their parents' wishes regarding adherence to their faith-based traditional teachings about education. At that age, teens still need their parents' guidance, rather than a permissive attitude of let the kids decide what they want to do!
Where would you draw the line, or do you have one, with respect to parents enforcing religious doctrine and/or practices on minor children?
Parents come first, unless, of course, they are being physically or emotionally abusive towards their children.