I don't know how much the original creators thought about it other than a plot device for a means for Robuttnick to weasel his way into a position of power with King Max. The overall ambiguity of this ominous "Great War" does give me a feeling of wanting to know more; I pretty sure that they were going to cover more about it in the third season that never happened.
However, you can be assured that it would probably be involving two or more factions vying for resources or religious beliefs. When you get down to the nitty gritty those two factors are always at the very basis of all human conflicts. In Sea3on we know of at least one, or possibility of the only the main adversary of the Mobotropolian people: The Warclaws. Though not much has been revealed thus far about the hows and whys of the conflict, either or both of those factors could be the cause of the conflict.
I get the feeling from SatAM and Sea3on that The Great War wasn't going well for Mobotropolis and Julian came in, and with his technology, turned The Great War to their favour. With the order of King Max to "dismantle the military" in Blast to the Past leads me to believe that Mobotropolis might not have had more than a meager defensive force to begin which would leave them wide open for conquest until Julian came to the rescue.
Mobotropolis, just by how it's always referred to as a city rather than a country might be a city-state similar to something found in Ancient Greece; i.e. Athens. Perhaps they were a small "utopian" oasis in an otherwise hostile world filled with many factions that were at eachother's throats and were caught in the fray.
In both Cry of the Wolf and Fed Up with Antoine we were shown two other factions: The Wolfpack and The Nasty Hyenas. Now, it does mention that the Wolfpack is loyal to The King "Max," but The Nasty Hyenas are a pack of wild vagabond cannibals; perhaps they were somehow allied with The Warclaws? Other than the Terapods, which I really wouldn't call a faction, I don't remember any other groups that were not somehow affiliated with Mobotropolis or The King.
As far as geographical areas in SatAM, most seem to be uninhabited by name: The Great Unknown, The Great Forest, The Great Swamp (that has a prison that has been abandoned for over a millennium: Ironlock). Come to think of it a lot of things have "The Great" preceding it in name; perhaps that in and of itself might tell a lot about the Mobian psychology.
Anyway, that's my 2 cents on the topic.
Let me just say your input was worth way more than two cents. Very observant!
You are right about civilizational conflicts. They can be boiled down to a mixture of resource-based and broadly ideological issues. Most mainstream historians prefer the term “ideological” as a broader and more accurate term over "religious” conflicts however, seeing historically how secularist like Pol Pot's Khemer Rouge and Stalin’s Militant Atheist League (yes, sadly that was a thing) have spilled a lot of innocent blood in our own history’s past just as much (if not, way more than) various religious ideologies. To use some real world examples: even today radically secular North Korea punishes Christians up to three generations, placing the believer, child, and then grandchild in work camps 
! And the total of diverse religious peoples persecuted by certain anti-religious political parties has skyrocketing into the millions (over 12 million for just Christians in the old USSR alone, that’s not including other religions and locations getting the axe). Heck there is even internal denominational-conflict between irreligious communities (atheism is divided into three quarrelsome groups of Classic, New, and the less aggressive, pro-theist “3.0” movement). And I thought the crusades were sad… 
In reality all you need is one small disagreement, between two disagreeing people, and only one disagreeable person to start a fight. On a side note, that is also why the internet has so many silly flame wars over trivial things! Give people the ability shoot each other over the internet and there would be war in our own diverse fandom everyday! 
That’s enough philosophizing for me today. In a nut shell, I guess what I’m trying to say is that any difference of ideals can lead to a nasty scrap (fortunately, that gives us lot to work with storywise). Now that is clarified and were not thematically limited to jus relgion vs. religon based conflicts, let’s get to the other good points you made and how they apply to the rules of civilizational conflict.
The Hyenas: These nasty fellows are real amoral to be eating their own kind for the hell of it. Obviously they are some form anarchists (hence why they typically eat their effigial “leaders” in the same – but all more intense - way people in our world mock politicians on SNL and with cartoon caricatures). I would bet my bottom dollar that they were either an extreme reactivist group that was fed up with the Acorn dynasty (if they were pre-coupe) or a group akin ideologically to the raiders of Fallout Three (post-coupe). If I was writing them, I'd play them as a radically anti-authoritarian wildcard that hates everybody but themselves. And even with that said, they would be internally unstable.
The Wolf Pack: If they are and were loyal to the Acorn Monarchy, it’s because of Max’s centralist and anti-colonial policies. Being the type of guy who disbands his whole military (which in my opinion was a very, very dumb idea - *points at what use to be Mobitropolis*), King Max must not be a big fan of expanding his empire, unless this was all some clever political rouse. Deceptioin could still be a possibility, I have my suspicions. That means he probably doesn't make a lot of enemies with indigenous peoples due colonization. Perhaps The Wolf-Pack is a long term ally of the old kingdom, both of them having a good history (like America and England since the 20th century)? Maybe Max and previous monarchs have supported the Wolf Pack before due to some common interest and that has lead to a strong bond. Any ideas on what that could be?
