In canon, angels are not in conflict with each other. All the angels that ever would rebel have done so. Additionally, there isn't angelic politics, since all angels have a job to do, and when they've done it, they go back to heaven to praise God, so they don't have any spare time to get into mischief. Angels are directed by the ineffable wisdom of God and are miraculously guided to do his Will.
I don't see that as a conflicting translation, especially not given the self-perceived position of the Church at the time.
Just so everyone is clear, the Cathars were not just "another Christian sect" in the eyes of the Church, like the mendicant orders of Franciscans, Carmelites, Dominicans, Servites, or Augustinians, all of whom were also "poverty-based" and all of whom arose about this same time.
The Cathar doctrine was radically opposed to the existence of and a direct challenge to the authority of the Church. First, they were heavily influenced by Manicheanism (an early Christian heresy in itself), the belief that Good (God) and Evil (Satan) were (more or less) two balanced forces, that God was not perfectly omnipotent, and so there was no guarantee of victory of Good over Evil. This alone would have been enough for a person to be in trouble, but the Cathars took it to another level, the "dealbreaker" for the Church.
Their premise was simple (and I may be oversimplifying, but I'm close enough) - Adam and Eve fell from grace with God, and Satan was left in charge of The Garden of Eden, which became the World as it is now known. Thus, everything in the world is corrupt, every institution of power corrupted by Satan long ago. God's world is in the next life, and this world is the domain of Satan, the "earthly" as opposed to the spiritual.
Thus anything "material", including earthly power (read "The Church") was an extension of original evil, and only the spiritual (love, faith, the next life) were Good.
And, given many recent acts of the Church and the general state of the world, this wasn't hard for many to believe.
This was very popular with some nobility because it meant they didn't have to recognize existing power structures, since they were all "Evil". And this was very unpopular with most of those existing power structures, including (but not limited to) the Church. The fact that some of the most unspeakable acts were committed during the Albegensian Crusade only adds blackest irony to an already twisted act, one that lost the Church much of what little temporal respect it had in the centuries to come. (But that's historically what you get for saying that any dominant Religion is "Evil" - they just go and prove it, again and again, until anyone implying such regrets is or is dead.) 
So - to keep this on topic (or not entirely off, at least, ahem), Domain Lore would indeed have nothing to do with this sort of division. Angels still work the same, miracles and Faith still work the same. And most trained Theologians would "know" that any sort of Manichean dualism is rubbish, that God is omnipotent, even if his plan and reasons for creating a world with Evil are also ultimately unknowable. It would take [u]either[/i] a very naive theologian or one with huevos grandes to disagree and get as extreme as the Cathars, Bogomils and Albigensians.
Sorry to be critical of a game which I really do like very much...but the Dominion Lore thing is one more example of where AM diverges from anything medieval people actually believed. You'd be hard pressed to find any medieval writers who actually believed all Abrahamic religions were divine. The closest would probably be early Muslim thinkers, and even they were far from considering religions equal. It's pure "Mythic Europe", as opposed to Medieval Europe.
That's intentional, and I think more Mythic and less Paradigm would actually have done the line good (I know I'm probably in a minority there). I just think the perfect unity in Heaven, which Alex White rightly noted is canon above, is less productive to the game than uncertainty and division.
Yes the “Medieval Paradigm” is supposed to be based on how the medieval people perceived the world, but you have to remember that Mythic Europe is a big place. It contains a lot more then Christians and the ALL thought they where right. So writing the Dominion so that all faiths appear valid (at least to themselves) seams more in keeping with the paradigm then choosing one religion to be favored. Plus it allows for a richer game setting opening up characters and plots based on other religion and the faithful therein. Not to mention the friction between them.
There's also the problem that expressions of the Divine realm are a frequent occurance in Mythic Europe, making Dominion Lore (or a similar ability vital to the setting).
In game terms, however, I don't find DL especially problematic since, in practice, a Christian (for example) would find many of the manifestations of the Divine that are associated with the Jewish or Muslim faiths substantially weaker or non-functional for him. From this perspective it might be decided that whatever meagre spark of the Divine exists within lesser religions is a result of deliberate or accidental similarities to Christian practices...
Similarly, I've always pictured Divine characters as dividing the realms as they perceive them: Those that aid their powers (Divine) and those that don't (Faerie, Infernal and Magic). As such, I imagine they'd be somewhats skeptical about the existence of Faerie and Magic as distinct realms. Particularly in light of the Infernal's affinity for deception...
...and maybe they're right! 