Catholic Church and the Critique of Pagan Worship? There has and still is a major Critique of The Catholic Church when it comes to doctrine around the Pope and the leadership structure and also what is seen as the worship of Mary, you may also add the statues that were remade from pagan gods into the saints of the church. The critique is large and it often comes from the rest of the Body of Christ (the church).

I will confront the question from the view of Sun god worship. Common knowledge that change came with Constantine (not a controversial view of History). Suddenly  "Christian Holy days" match with pagan dates and even more controversial the structure of pagan worship does match as well.


The structure of the leadership in connection to the story of Nimrod 
You see the round wafers in the sacrament and in the monstrance symbolize the sun (the sun was erected above the altars in the worship of Baal)
The wine turns into blood (drinking blood) not just a symbol
The columns of St Peter's Basilica in Rome have a sun-like image, and a wall has a golden sunburst image just as in the Babylonian temple


So much to say and has been said. Many books on this critique or just plain history books.

The question here is how does the Catholic Church deal with this problem. Are there any books, sermons, teaching or maybe you can present the full answer below, How does the Catholic Church deal with such questions, that is one question, the strong connection with pagan worship or the accusation of it?
Cardinal Newman, the leader of the Oxford Movement in the Church of England who converted to that of Rome in 1847 wrote a book entitled An Essay in the Development of Christian Doctrine.

He describes the problem in Chapter 8, Section 2, Paragraph 12.


  That great portion of what is generally received as Christian Truth is in its rudiments, or separate parts, to be found in heathen philosophies and religions.


He lists amongst these a doctrine of the Trinity, the ceremony of washing, the rite of Sacrifice,  the Divine Word, the doctrine of the Incarnation, angels and demons, a sacerdotal order and a new birth.

He says that Mr (Henry) Milman argues from this that


  These thing are in heathenism, therefore they are not Christian


but that we (Cardinal N and the RCC) prefer to say


  These things are in Christianity, therefore they are not heathen. 


He explains


  From the beginning the Moral Governor of the World has scattered the seed of truth far and wide over its extent, that they have variously taken root and grown as in the wilderness, wild plants but living; and hence that as the inferior animals have an immaterial principle in them, yet have not souls, so the philosophies and religions of men have their life in certain true ideas they are not directly divine.


A little later he says one way Providence has imparted divine knowledge to (the Church) is by allowing her to draw and collect it together out of the world and so to suck the milk of the Gentiles.

In so far as this question is a resource request, Cardinal Newman is someone who addressed this issue.