What is the ruling on the slaughter performed by a child whose parents are both polytheists (Wathani) or dual-worshippers (Majusi)?

Primary text

According to the core doctrine of the three Imams (presumably Shafi'i, Malik, Ahmad, based on context), the slaughter is forbidden. However, the view attributed to Abu Hanifa is that the slaughter is permissible in all circumstances because the ruling is dependent solely upon the religion of the slaughterer, not the religion of the father. This is supported by the fact that determining eligibility for Jizya is based on the slaughterer's religion, and by the general text (of permissibility) and analogy.