I think American Christians should do neither. Restricting a child's access to information in order to indoctrinate them into a set of beliefs unquestioningly is a form of child abuse. Various forms of psychological and physical abuse are extremely prevalent in American Christian parenting practices, and it's something as a society we should not tolerate.
Exposing children to propaganda that they are ill equipped to deal with is also child abuse.
Just because someone can argue better than you can does not mean they are right. Climate change deniers can be very convincing if you don't understand physics.
