My fault for not expressing myself clearly - I was not sufficently clear when I said "You're not born Amish".

While Amish people do have children, and they take their children to church, the children are not members of the church. That takes place as an adult. So the children are part of the Amish community, but not the Amish church.
<sigh> That still reads as clear as mud. Some days it's just not worth firing up the ol' computer.
For more info that you could ever want on the subject, see
http://www.amishnews.com/amishseries.htm. The articles on this site are fact-checked with local Amish, so they should qualify as an authoritative source.