One connection is how to train your baby books I mentioned. The foundation most popular book is named "To Train Up a Child". They are literal Christian child raising books that teach how to property spank. These and similar books/approaches are recommended inside fundamentalist circles, unknow or controversial outside them. Christians openly advocating for these approaches is just normal in more fundamental circles (by which I mean I personally knew such people and they are not even all that much fundamentalist, just tilted that way).

you don't recognize there's any sort of historical pattern between religion, at least w the more extremist parts, and punitive punishments? conversion therapy, Indian boarding schools, child wilderness camps, Catholic sex abuse scandals are just a few that pop to mind