Ditto to all of the above.

Sad to say, but no matter how wrong they are, parents will generally not let you tell them how to parent, and a nanny is expected to be an extension of their parenting "style," not a challenge to it.

You've obviously taken a job with parents whose philosophy is diametrically opposed to your own. It matters little that theirs is dead wrong; they're the boss, so the best thing you can do for yourself is find another boss.