This has many of the marks of Gnosticism. The prevalence of the number 13 (prevalent in Freemason symbols and rituals) and the forcing of asceticism on the children. It is possible that the parents thought that by forcing these harsh conditions on the children that it would allow them all to ascend to the "realm of light". Here is a description of one of the medieval ascetic sects of Gnosticism that seems relevant:

The Cathars apparently believed that people could be reincarnated. Reincarnation was not however a desired event. The goal of the Cathar was liberation from the realm of limitation and corruption identified with material existence. The way to escape was to live an ascetic's life, a life dedicated to standing apart as much as possible from the material world and its many evils.

Those that did live this life were called 'Perfects' (Parfaits). By virtue of their noble dedication, they had the power to aid others to break free of material enslavement so that they might upon death achieve liberation and return to the realm of light that was their true source and ultimate destination. The Perfects themselves lived lives of unimpeachable frugality (this due to their belief that the material world was evil). Commonly, the wiping away of sin, called the consolamentum, was performed on someone about to die. -- http://www.sullivan-county.com/id2/gnostic_files/cather.htm

Also, as with many of these deranged Gnostic based religious groups, you'll notice that much of the blame is not being specifically alleged to be due to Christian beliefs, but it is certainly being implied by much of the news coverage. This is a common tactic used by Freemasons and Mormons. They say they aren't really Christian, but they kinda are. The concept that it is acceptable to lie or perform any kind of horrible act to promote "the greater good" is very prevalent in Gnostic beliefs.