How to formally state that parents have not raised their children well

Irresponsible

This should fit the bill of describing the core issue, whilst not judging manners broadly, nor performing character assassinations.

I think dysfunctional is also insufficient because functionalism can come under heavy debate.

The same issue would come up if you wanted to express any other negative thing about a person in a formal, polite way.

The truly descriptive words might be things like "incompetent" or "irresponsible". But those are clearly highly charged words.

The common way to make such statement more polite is to tone them down. Instead of saying someone was "incompetent", say "they were less than completely competent", etc. That works in a personal conversation where the other person will likely understand what you mean. I'm not sure it works in the kind of scholarly discussion you're describing, where it could be taken literally -- they had minor failings -- rather than as a polite understatement.

Still, anything truly descriptive will be harsh.