Playing devil's advocate here, could it be that they ran something like a baby euthanasia outfit? like, no contraceptives back then, extreme social stigma surrounding birth out of wedlock, poverty forcing women to give up their newborns, giving them up to the nunnery, which had no resources to deal with feeding caring and raising thousands upon thousands of children, and so either A) simply took it upon themselves to take the logical step and cull some of them, or B) that a high number of babies died of natural causes (neglect, malnutrition, sudden infant death syndrome, disease, whatever) and they simply disposed of them.
I don't know what else could explain this, it's not like we're seriously talking about gangs of murderous baby killing nuns roaming the streets at night and snatching up babies by the hundreds for lust murders, right?
As far as I'm concerned, the only crime here is the institutionalized psychopathy of a religious patriarchal system that refused to take responsibility for giving people a legal and moral avenue to raise children that were brought into life in violation of religious law.
Makes more sense to me at least, I may be fuck way off wrong.