There is really nothing to reconcile, since there is nothing contradictory in these doctrines.
Jesus revealed to us, “Unless you are born again of water and the Spirit (ie, Baptized), you cannot enter the Kingdom of Heaven.”
The Church has always taught this (and still does). But there’s a “mercy problem” when considering the death of unbaptized innocents.
If one takes the Bible literally, as some protestants do, there is no question at all. Jonathan Edwards, the great Calvinist preacher, wrote in his famous sermon, *Sinners in the Hands of an Angry God *(one of the masterpieces of the English language), “The road to hell is paved with the skulls of unbaptized babies.” What a grim picture!
Catholic theology, however, recognizes a distinction between innocent and not-so-innocent unbaptized persons. This is why the Church is always careful to point out that the fate of the innocents is DIFFERENT from the non-innocents.
We do not know exactly what that fate is - we don’t know what those “differences” are. For awhile, Catholic theologians played around with the idea of a semi-hell called Limbo. Limbo would not be an unpleasant place - it was supposed that a soul in Limbo would experience the fullness of natural happiness (ie, the type of happiness we may enjoy on earth) but would be denied the fullness of supernatural happiness.
Such a person might be compared with a king in the Middle Ages. A king surely thought he was living the good life - even though his bed had fleas, his castle was drafty, his means of transportation was a horse, and his main form of entertainment was a clown in a silly hat. This king could not even imagine the wonderous lifestyle that even the middle-class enjoy today. If the king COULD imagine such wonders, he might feel his own lifestyle was lacking in many respects. But since he CANNOT imagine such things, he is quite happy.
However, most theologians have abandoned the Limbo idea in favor of simply saying, “We don’t really know what happens - we pray for the best.”
The Church has never precluded the possibility that the unbaptized innocents may have some opportunity for salvation even in the next life. After all, Jesus went to some place of unbaptized innocents (the “Bosom of Abraham”) between his death and ressurection.
So the Church encourages us to pray that innocent people who die unbaptized will somehow attain their salvation, just as those ancient unbaptized innocents were able to do.
We simply don’t know how or if this is possible (because God has not made these specifics known to us), but we hope and pray for the best and let God work out the details. Which is exactly what CCC 1037 says.