Shakedown

At the risk of beating a dead horse, I'll take a few more whacks with the meat pounder: It's my impression that many Catholics are Catholic because they think their sect is the repository of salvation. Given that outlook, I think many Catholic parents have a cynical, calculated attitude. Child abuse is the price they pay in exchange for salvation. 

An acid test of friendship is putting people in a competitive survival situation. At the most generic level, the quickest way to turn neighbors into murderous adversaries is when demand for some essential good or service exceeds supply. "Friends" and neighbors turn on each other.

A cheesy variant on this theme is the Jem'Hadar, who are dependent on a supplement ("the white") to stay alive. That ensures their allegiance to the Founders.

Or consider the literary trope of the village that makes an annual offering of sacrificial virgins to the local dragon. If they don't placate the dragon by human sacrifice, it will incinerate their crops, causing famine. Another example is Shirley Jackson's notorious The Lottery.

Even though those are fictional examples, they have a lurid basis in reality. Historically, pagan parents did practice child sacrifice to appease the gods or solicit their favors. 

For all their outrage, Catholic parents reflect the same ruthless quid-pro-quo. Child abuse is the unfortunate but necessary payoff to secure sacramental grace–like protection money.