You may have thought that public schools in New Zealand do not include religious indoctrination. The fact is that over 40% of public primary schools run religious instruction classes run by outside volunteers from churches.
Schools have no obligation to ask parents permission before including children in religious instruction.
Regardless of the religious beliefs of a parent their children can be included in religious classes without their permission. For example, if a child has parents of the Muslim faith and is sent to a public primary school as required by law, the school can include the child in Christian religious instruction classes without the consent of the parents.
Schools have no obligation to inform parents of religious instruction.
There is no requirement for schools to inform parents that religious instruction out of formal school hours is taking place. It is often the case that the first a parent will know about religious instruction will be children coming home with religious materials or asking questions about religious doctrine.