One of the most strange and shocking things Karl Barth said (and he's said a lot of them) was the only difference between Protestants and Rome was the doctrine of analogia entis and that this doctrine was from the anti-Christ. He said this in between the radical days of his Romerbrief and the beginnings of his Church Dogmatics, after he rediscovered the heritage of the Reformation. von Balthasar, and other more conciliatory students, argue that Barth softened on this point and misunderstood what he was fighting against. von Balthasar et al. sometimes even argue that Barth softened his opposition. When understood through Pryzywara, who taught von Balthasar, then the doctrine is sound. I'm going to tentatively disagree.
The analogia entis in brief is an idea that rests upon Absolute Divine Simplicity. This is the idea that God as Simple (as in not made of divisible parts) requires a metaphysical equal signs for realities that seem distinct for men. Thus, while good, beauty, justice etc. are distinct categories of Human thought, in their Divine true sense, they are all one in the same. However, this is neither understood equivocally or univocally. That is, what we say of Human good and Divine good are not two radically different things (equivocal) or that the Divine good is the maximal form of Human good (univocal). The analogical understanding is that there remains a similarity that exists in an infinitely qualitative difference between the Human and the Divine. Thus, Human good is like Divine good, but it is not Divine good. This is, mainly, because Divine good is itself Divine, namely God Himself. The horizons of Human understanding see the conflation of categorical distinctions, and we see the hazy reality that exists beyond all Human concepts of knowledge. The horizon is itself not the edge, except in the sense that it is edge of created reality, a reality that the Divine can intersect and meet us in. The finite cannot broach the infinite, but the infinite, lacking any boundary set on its ability, can intersect the finite.
The fundamental reality from which all categorizations flow is the primary category of categories, being. This is the easiest way of understanding the analogical difference. While Humans are beings who exercised such in becoming (we exist and we move from is to is not), along with all other created things, God is not a being, but Being Itself. This means God is not merely the biggest and best piece of furniture in the room, but is the very grounds of existence (to say the room in this metaphor is not itself enough).
None of this is distinctly Christian. Plotinus, the mystic and Neo-Platonist par excellence, argued something similar in how he conceived of the One. You can even see a pseudo-trinity in how he talks about the One, the Nous/Mind, and the World Soul. Some Hellenophile Christians embraced Plato and his students as God's prophets to the Greeks (Clement of Alexandria). Others accepted the metaphysics in a more qualified sense (Origen, Justin Martyr), but it's here where problems emerge. As I've said elsewhere, Origen was the first to understand all the problems and lay them out clearly, and simultaneously proceded to answer them in all the wrong ways, revealing the fundamental problems between Hellenistic metaphysics (which had all converged into late Middle and Neo Platonism) and the Holy Scriptures.
While a major problem with the analogia entis is the subsequent Absolute Divine Simplicity it entails, this is not the only one, which has more serious ethical implications. Rather, it is how the universe is conceptualized. The analogia entis recognizes a kind of Chain of Being metaphysics which implies a kind of harmony within the World. Humans, who possess a sense of divinity (whether in Plotinus as divine-spark or the more Biblicized notion of Image of God) can ascend and descend along the ladder in a quest towards reunion with the One, who remains always out of sight and yet always close. Thus, Plotinus can paint a picture of the infinite quest of the alone chasing the Alone, but he can also speak about experiencing the One because of the One's effulgent presence of the Good.
In addition to this, the One as ultimately simple and as the ultimate good, only meditates (if such a word is proper to use) on itself as the only One, literally, for nothing else is worthy. This is the goal of all Humans as well, who fix their eyes upon the One who sets its own eye (again, an anthropomorphism) upon itself. Humanity's ascent is through this concentration, and its descent is through taking its eyes off of it.
However, none of this squares with the Biblical portrait of God who looks upon the deeds of Man, knows the very hairs of his head, and condescends to him in providential lovingkindness. Neither does this square with a Creation which is in a state of corruption, threatened with oblivion, and is a de facto war-zone. In fact, the world of the analogia entis promotes a conservative view of the hierarchy of the world as it is now. It is individual Human fates that ascend or descend along the ladder of proximity to Being. Origen's answers that imply an infinite cycle of falls-and-redemptions and the pre-existence of souls are attempts to answer clearly Biblical problems, but trapped within Hellenistic metaphysics. It also explains why he can sound proto-Nicaean and proto-Arian at the same time.
This is why it might be right to call the analogia entis a form of anti-Christ: it denies the radical depth of corruption that Adam plunged the Creation into. It individualized a corporate problem, and simultaneous banishes the Fall while it makes it inherent within creation due to finitude. In this way, Origen, and Augustine who continued the same metaphysic, are kissing-cousins with Schliermacher who posited that man was created in sin. Finitude, individuality, and free-will become the prime reason for the fall and sin and redemption tends towards erasing all of these. If you read carefully, it's hard not to see the Beatific Vision as a form of Death, a parallel to Nirvana, where the mind is totally fixed upon God/Being/One and, in a way, snuffed out. To the Image of God, creation is itself a distraction. This is a doctrine of demons.
This is why I have become recently fascinated with the 17th century Confession of Dositheus, an Eastern Orthodox response to the supposed crypto-Calvinism of Cyril, the Patriarch of Constantinople. The response is so obviously colored with misinformation and Roman Catholicized doctrines that is somewhat bewildering. This is clear in the Molinistic Arminianism is professes, in God's saving grace takes place by forseeing the faith some would have.
What does that have to do with the analogia entis? Because the idea of a predestination conditioned by foreseen faith places the foundations of the Creation firmly in a harmonious universe, a kind of best-of-all-worlds theology which Voltaire, in Candide, mocked rightly, even if he was mostly biblically illiterate. This idea makes a mockery of divine justice, it becomes a court-room that only prosecutes entrapment. It doesn't take serious the weight of sin as the threat of hurtling all creation into the void.
However, this does not mean God does not have providential mastery over all things, but He does in a way that does not conflate God with the stability of the World Order. God cannot be Creator if the Creation disintegrated because it means that either there was a time when God was not the Creator (which means God changed ala. Process theology) or God, as Absolutely Simple, would cease to exist if He ceased to be Creator (as all names and categories are the same in Him). Rather, there's an alternative solution that has remained in the Orthodox energies-essence distinction, one that makes sense between the realist ontology of an analogia entis and a Nominalism that makes God totally alien to all creation.
But I digress. God still remains sovereign over His world without having to change (for that implies imperfect), but it's because the analogia entis is wrong. This is why David Bentley Hart, who I enjoy reading, seems caught between Christian Neo-Platonism, through Gregory of Nyssa, and a sort of Manichaean Dualism of Cosmic Warfare. His saving grace is the incoherence of the two, as it is like jamming two crooked houses together, doesn't seem to come apart except before Calvinist critics who question how his latter emphasis isn't just Manichaeism. In some ways, the charge sticks.
However, and to this is to the point, analogia entis straight-jackets all cosmic warfare in a universe that is fundamentally at peace, but is disrupted by enemies. But Christ has ascended on high, and rules at the Right Hand of the Father, until all His enemies are made a footstool. This reveals a Creation that is not in harmony. St. Paul says the Devil is the god of This Age. Does that sound like the stupid Christian Neo-Platonic synthesis that Hans Boersma discusses? The Middle Ages was not proto-Paradise, but a Hellish display of brutal oppression, with prince and priest hand-in-hand.
This leads to different views of the Christian's place in the World. The Biblical view places us to see a Creation divided which needs the saving reign of Christ, where God will liberate and redeem all those under the chains of the Devil.