Anselm’s theory of atonement is one of the pet peeves (to put it mildly!!) of the Eastern Churches. The bottom line is that it was unknown in the Church for the first thousand years, and for this reason it is a doctrine found only in the Catholic and Protestant Churches.
Just to say a few things in explanation of why the Orthodox will have no truck with Anselm and the atonement theology which he developed. I am reluctant to get into it too deeply - past experience has shown that there can be a negative reaction from Western Christians, both Catholic and Protestant, because they feel that the Orthodox are attacking one of the bedrock beliefs of the faith.
Anselm’s writing of Cur Deus Homo was a significant development in the West (we even had to study it at Catholic high school), but it did not affect the East at all. It profoundly changed the Western theology of the
atonement. For hundreds of years afterwards Western theology, Protestant as well as Catholic, traced its soteriology (the understanding of salvation and how we are saved) back to Anselm. Because of the split between East and West, Anselm’s theology had little or no influence in the East.
For this reason, Orthodox Christians tend to see Catholics and
Protestants as having far more in common with each other than either
does with Orthodoxy.
Anselm developed what has been called the “judicial” theory of the
atonement. In his book he sought to answer the question “Why did God become man?” He found the answer in a concept in the mediaeval law of his time - the concept of satisfaction. If one person wronged another, it harmed the other person’s honour, and so the wronged person demanded compensation, or “satisfaction”. Man’s sin had offended God, and because God is infinite, and God’s honour is infinite, the insult man’s sin causes to God’s honour demands infinite satisfaction. But man is in no position to provide this satisfaction, so God sent his Son to offer the satisfaction on behalf of man. By dying on the cross he appeased God’s wounded honour, and made the full and adequate satisfaction for man’s sin.
Of course you know all that already, and it is a very much oversimplified (but accurate) account of Anselm’s theology, as it has developed in the West, but Orthodox theology knew little of this. The Western theological development stressed salvation from an angry God, whereas Orthodox theology stressed, as it always had, salvation from sin, evil, death and the devil.
But doesn’t this sort of beg the question if Jesus’s Incarnation, including His act of sacrifice and resurrection, reversed the consequences of Adam’s sin? If, IOW, “sin, evil, death, and the devil” would still be our lot if not for Christ’s advent, how was salvation accomplished? What changed and why? If Jesus hadn’t conquered death then we’d still die. But why would we still be subject to death in that case?