The really short version is that it doesn’t interfere with God’s mercy, but we cannot be absolutely certain what that means for the children involved. It may mean that God saves them all in a blanket act. It may be that God saves each one, but in an individual case by case determination. Or it may be that He doesn’t.
My attempt to explain my understanding:
By his sin, Adam damaged his nature which we inherit. We do not inherit guilt for his sin in the same way that we are guilty of our own sin - babies are not guilty of eating the fruit.
But part of the damage that was done to human nature is a removal from our natural state of grace - we are no longer born in a state of friendship with God.
This is why the idea of limbo came up - babies committed no sin, so they suffer no punishment in hell, but they are not in a state of grace so they do not enter the beatific vision. This idea came about because there must be justice and mercy: no one deserves heaven, and the children experience perfect natural happiness because there is nothing they need to be punished for.
And I think that idea would be just. That is what I, personally, would expect to happen in the absence of extraordinary action by God. However, because we know that God is merciful, and because we know that God loves us all, especially children, we can have a reasonable hope that He will take such extraordinary action and save such children before they die.
Key points - we cannot expect extraordinary mercy from God, as something that these people deserve to receive. No one deserves anything from God, aside from what God has decided to give him. So in this way we cannot say that God somehow must save infants, or definitely will. Mercy is by definition undeserved, if we knew that the infants deserved special treatment and would certainly receive it, it’d be a matter of justice not mercy.
But on the other hand we know that God is merciful and does dispense His mercy liberally, and so we can have a very real hope - a hope that borders on expectation - that God will save infants. We just cannot say that He is required to.
Or in short - Children will not be punished for their fathers’ sin, though they will suffer effects of it. Thus even if a child dies and if God does not take him to heaven, the child will not suffer punishments because he did not do anything to be punished for. However, I hope and almost expect that God will mercifully save unbaptized infants, and this is a reasonable hope to have. But however reasonable such a hope appears, we cannot count on God to save people outside of the ways He has said He will, and so we cannot say that we know that He will save unbaptized infants.