Just opinion here, but ultimately children have the same religious rights as adults, it is their liberty to exercise those rights independently that is severely limited by due process, as the law recognizes almost total parental control. Children can be forced by parents to attend religious schools, churches, etc or conversely not attend against their will, even if they are not mainstream recognized churches(think David Koresh/Waco). Children have even died as parents "exercised their religious rights" by withholding medical treatment from their children. Courts vary as to how they view all the varying cases.

Certainly the state has an interest in cases of physical and mental abuse, but rarely does it exercise this interest in children who are subject to what many of us might consider mental abuse at the hands of religious fanatics and zealots. Children can sue for emancipation or self-emancipate, but it's pretty rare, and the younger they are the more difficult this obviously is. Here's a link with a New York case that may help:

http://www.icsahome.com/infoserv_art...ation_laws.htm

Dig a little harder and you'll find lots of info.