They would never perform an exorcism on their baby.
You might think this is uncommon, but I don't know how uncommon it can be when I personally know someone who had a crazy aunt living with her who was determined to drive evil spirits from her, and abused her in all sorts of terrible ways to do so - Evil spirits she believed were in my friend because her mother died giving birth to her.
Uncommon or not, it happens too frequently.
I ferverantly hope that such things become less and less likely as time goes on.
(Hat Tip: Pharyngula)