Coming from the Reformed background- I know the concerns of Christian and non-Christian parents regarding their children. My four children were all infant baptized.
It is fear that sometimes motivates us -especially when our children are still young and sort of weak-we want thenm protected from sickness and death. More so from the power of the devil. This must be addresed by the beliver’s baptism group such as I am now.
One must not take refuge in supposed innocence or spritual purity of infants. The doctrine of original sin demolished such arguements. We cannot also take refuge in a Universalistic views of salvation -for this will minimize the uniqueness of salvation in Jesus. Though we might have to ascertain if original sin means also transmission of Adam’s guilt. We must analyze the verses at Psalms and as well as other didactic protion of the Scripture if this is so.
I am more incline to find comfort in the doctrine of Election and Definite Substitutionary Atonement as seen from the New Covenant perspective-since it is leaning more in the finished works of Christ and his forerknowledge. Meaning, Jesus knows those who will die in infance and thus made provision for them-whether children of believers and unbelievers.
Thus one need not accept covenant theology and infant baptism just to be sure about their children’s salvation when they die during infancy.
I have qualms about infant baptism used in this way-it seems to degenrate to ritualism, superstition and seems a little “faith plus works” salvation. And it tends to minimize the importance God’s ordinance of baptism instead of magnifying it. But more on this later.