Actually that's not what the nuns taught us in Catholic grammar school in the 1950's. Jew's and others persons sitting in darkness without Cross or Law could get into heaven based on "Baptism of Desire", i.e., trying lead a good life, rather than mere "Baptism of Water". If anything the obligations on believers was greater because God had chosen to let us in on the secret. But babies dying without Baptism were condemned forever to Limbo, where they would experience all the joys and pleasures of Heaven but be deprived the "Beatic Vision", the sight of God. Which is the worst that could happen to a just Pagan.
This is what O'Reilly claims HE was taught in Roman Catholic school also.
I propose a way to settle the matter. How about we hear the words of JESUS CHRIST HIMSELF?
John 14: 6Jesus told him, "I am the way, the truth, and the life. No one can come to the Father except through me.
Pretty straightforward and clear.