Pope Benedict XVI disliked the idea of Limbo for unbaptized children, and was a vocal supporter of leaving it to trust in the mercy and goodness of the Lord and His great saving power
but as far as I know, even though Limbo is an unpopular theory, it is still an acceptable world view for a Catholic
One of the beautiful things about our Holy Catholic Church is that she is able to hold under the umbrella of
Orthodoxy a variety of theological opinions, speculations, and theories. She has always done this, from in the earliest centuries of Christianity to the modern day through a magnificent diversity of
autonomous local Churches, each having ancient modes of understanding the
One Faith. All tolerated theological constructions that have been or continue to be used in the Catholic Church however must align with defined dogma, which, we believe, as once and for all given to the Church by the Blessed Apostles and is formulated in new (but essentially the same) ways over the millennia by the
Magisterium.
Limbo is one of these tolerated beliefs. It does not appear to have had a strong pedigree in terms of the Early Church, but that doesn't make it any less useful since the word "Trinity" is scarcely mentioned in the early Ante-Nicene period. It
seems that in ancient times, Christians generally assumed Heaven for unbaptized children born in the confines of the Church, as it were. The
Eastern Churches reflect this since they have, generally always, given full Christian burials to unbaptized children born to Christian parents.
Yet, to make this (good) assumption a general theological principle is problematic because of the
dogmatic reality of
Original Sin. We know this from the Bible (Romans 5:12-20). All humans (with the Divinely miraculous exception of the Blessed Virgin Mary and the Incarnation of the Son of God) are conceived in a state of spiritual death, hence the need for the baptism of infants as soon as possible. We also know however that nothing unclean (sinful) can enter Heaven (Revelation 21:27). The Blessed Apostles simply did not tell us how to "resolve" this issue (perhaps it is none of our business?), and so the Church has developed ways of speculating about the destiny of unbaptized babies who die.
St. Augustine and others believed that they cannot experience the
Beatific Vision, but also that God would not consign them to eternal punishment. Therefore, they posited the idea that there is a state, or place, or both where the souls of unbaptized infants go to experience the absolute fullness of natural happiness possible without seeing God. "Limbo" as it were.
Other theologians, particularly in the East, did not agree so quickly to this as Western theologians did (though they did not say it was not possible). In recent years, most theologians have abandoned the theory of St. Augustine (which may actually be factual, we just have no way of knowing) in favor of a more "agnostic" position; that is, we
don't know what happens to unbaptized infants who die before becoming Christians – no more than we know what happens to unbelievers who never had the opportunity to hear the Gospel. We say however with St. Abraham our father:
"Far be it from thee to do such a thing, to slay the righteous with the wicked, so that the righteous fare as the wicked! Far be that from thee! Shall not the Judge of all the earth do right?" (Genesis 18:25). We trust that God, who is truly just and good, will deal gently and lovingly with all babies who, through no fault of their own, do not get to receive baptism before they die.
This newer (and, I think, better) understanding has been so overwhelming adopted by the Catholic Church that, to my knowledge, all the liturgical rites of the Church (including the Western Roman Rite) allow performance of Christian burials to unbaptized infants of Christian parents.
There are other theological dogmas under-girding this understanding (i.e. "baptism of desire" and the external application of faith to those who cannot believe), and so the International Theological Commission at the Vatican gave this
document as what we might call the normative (but not exclusive) understanding at current.
Hope that helps!