morality is subjective and people don't have free will

[brewer]

bold mine

Isn't enough that you/christians believe that they are? Isn't that one of the motives for infant baptism? It does not need to be taught to the child. You already believe it and that will come through in interaction with the child. 

I've heard parents teach their infants to pray from the time they can talk, pray to be forgiven for sin, even before the child can understand what they are saying.

(my bold)

Yes it is true that we do, but again, to most of us that is at its core simply the religious way of saying/explaining that none of us humans are perfect. That's the underlying principle, and I don't think anyone can disagree with it. I mean, do you think there is any fully functioning, grown human being who has never done anything wrong in his life? Never been rude to someone, never lied, never done anything selfish or petty, etc? No? We agree then that imperfection of that sort is the human condition. The difference lies in the way we explain it or word it. But the principle itself is one that we agree on.     

And even considering that, as far as I'm aware, the vast majority of Christian parents nonetheless view their babies and young children as precious and innocent, not as tainted and impure. Albeit knowing they won't be perfect, that's not how we view our babies and young children, and certainly not how we treat them or talk to them.

We're not talking about adults, were' talking about infants/children. 

At that point in their development they don't need to know about sin, let alone comprehend it. All they need to be taught is the morality of right from wrong as the parents/society sees it. Not that wrong = sin. They can't understand what sin entails. If wrong is equated with sin then I think you've given the child a burden that they will remember but don't deserve. Wrong should be considered a unknowing mistake. Example: Two year old's lie by unknowing mistake, not to commit sin. 

We're not talking about perfection, no human is perceived as perfect. We're talking about the perception of sin. By performing the ritual the child is perceived to have sin, not imperfection. There is a difference. If held by the parents/church/religion it can't help but color the interaction with the child. 

Sorry, in the context of this discussion you're going to have to tell me what you mean by innocent.