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For starters, you're participating in a religious ceremony that, as I understand it, is a way of symbolically stating your intention to bring your child up in the church. But you're not married yet. Generally the church favors doing things in a certain order: courtship, engagement, marriage, kids. So you have some catching up to do, I would think, as far as living according to church principles.
By similar logic you should criticize gay people who attend church, because "generally the church" favors people not being gay.
But even if this is a church that vigorously frowns on pre-marital sex and out-of-wedlock birth to the point of teaching the parents have jeopardized their immortal souls, it seems reasonable that the hell-bound parents might not want their infant child's soul to be in similar peril. Christening the child could save its little soul from a potential eternity in Limbo (which National Lampoon, as good a source as any, describes as "the place where dead unbaptized infants go and float around in a fiery lake that doesn't hurt as much as Purgatory"). The choice to protect the baby's soul from such a fate might seem like an obvious one to parents who are likely on their way to hell. So perhaps there is less inconsistency here than Cary thinks.