Explain to me why they can't allow their child to have some say-so over his, or, in most cases, her, body? Maybe he or she doesn't want pierced ears. What on earth would it hurt to wait until the child is old enough to make an autonomous decision? Even if the individual opts to let them heal over, there's still scar tissue there that didn't have to exist.
Outside of the ethical issues, why open your child up to the possibility of contact dermatitis, keloid formation, or possibly swallowing the earring? Don't babies have enough stuff to get through already? And I've read that infants have greater risk because their immune systems aren't fully developed yet.
I'm aware of the Hindu tradition on this, but on this one, I think practicality and the well-being of the child should take precedence over religious belief. Just because an action is steeped in tradition does not make it a just action. Sometimes tradition needs a swift kick in the butt with the boot of informed consent.
I say this as someone who made the conscious decision to get her ears pierced at around age 14 or so. The other immediate female members of my family do not have pierced ears. I think my mother was very wise to make me wait.