I think we’re getting a little sidetracked - there is an important discussion to be had, but perhaps there are three topics present:
(1) The fate of the unbaptized who are innocent of personal sin. The most recent ecumenical letter on this (to my knowledge) is
The Hope of Salvation for Infants who Die without Being Baptized from 2007, found here:
vatican.va/roman_curia/congregations/cfaith/cti_documents/rc_con_cfaith_doc_20070419_un-baptised-infants_en.html
A concluding note in paragraph 103:
What has been revealed to us is that the ordinary way of salvation is by the sacrament of Baptism. None of the above considerations should be taken as qualifying the necessity of Baptism or justifying delay in administering the sacrament. Rather, as we want to reaffirm in conclusion, they provide strong grounds for hope that God will save infants when we have not been able to do for them what we would have wished to do, namely, to baptize them into the faith and life of the Church.
(2) The fate of those who die unbaptized because the Sacrament - or indeed the very ministry of the Church - is not available to them. Such are counted among those who live in Muslim or atheist lands where evangelization is illegal or difficult. Not that we should not try, for such laws against preaching the Gospel are in opposition to God, but we realize that there are those who cannot be reached in their lifetime by our own means. We should first commend them to the Lord and pray for all who have not heard the Name of Jesus Christ to come to know Him through Providence. If we are still curious of how to reconcile a just and loving God with the apparent reprobation of these through no fault of their own, we may wish to take note of the theological concept of “invincible ignorance” for example from CCC 1793.
(3) This may be more of what the OP is asking - how common is the idea that there are those who
actually seek God but are condemned anyway. There is room for this within some parts of Calvinist theology, because of the emphasis upon predestination, but there is not universal agreement. I talked with a friend who is a Presbyterian minister and he noted “you will know them by their works” and that those who are predestined to Hell - positive reprobation - will not attempt to seek God. There is within Catholic thinking room for a type of predestination provided that it is not positive reprobation. In other words, if one is among the Elect, he or she is predestined so; if one is condemned, it is by his or her own actions. Jimmy Akin has a far better explanation in his short book, The Salvation Controversy.
I’ve also seen within some Catholics the idea that Marian veneration is a sign of predestination to Heaven, while those who do not practice it are condemned. In talking with Catholics who hold this view they often cite Louis de Montfort’s “True Devotion” but I think the saint’s arguments are more nuanced than that; otherwise we are to come away with Marian veneration as the core teaching and determinant of eternal fate. But such an idea does exist among at least some in the Catholic Church.