Interesting theory on "Catholic Morale" from Papa Clement which is historic. In that it is an accurate description of how the world should operate from the viewpoint of Papal Lawyers.
But to say the world should operate this way is not the same as how it does operate in real history let alone a game. For example:
1) Civitate 1053 - outraged by Norman (French) plundering Pope Leo IX excommunicates them and leads a 6,000 strong Papal Army including 700 Merc Swabian Infantry against the Normans who number 3,000 with another 500 local infantry Guarding the camp. Result Papal Army smashed by Norman Cavalry with only the Swabians putting up a hard fight. Pope is captured but is treated with respect by Normans who gain control of Naples, have their excommunication lifted and Papal blessing to take Sicily from Moors.
2) 1066 Campaign in England. Harold II of England excomminicated for Oath breaking and Duke William of Normandy gets Papal banner and blessing which does help with the recruiting. Harold II killed in battle and his Army defeated but only after it had marched length of England to smash a invasion from Norway then march back to fight a very long and brutal all day battle against superior numbers which is hardly evidence of crippled morale.
3) Bouvines campaign 1214 - Philip II Augustus who deeds include abandoning a Crusade, attacking the lands of a Crusader while he was on Crusade, having his agents treat a Pope so badly that he died and then locking a bunch of elderly Cardinals in a room with no food and water and lighting all the fires in the middle of a Roman summer untill the elected someone as Pope who was willing to agree to the Kings demands. Finally ends up facing an alliance of the Holy Roman Emperor, King John of England (who was a Papal Vassal at one stage), and the Counts of Flanders and Boulogne out to put a end to the evil deeds of this total B*****D (who the French still view as one of their best Monarchs).
King John who had problems of his own defeated by French Royal Troops near Angers while Philip II with 15,000 take on the Emperor and allies including William Longsword the Earl of Salisbury with 25,000 and smashes them.
4) Bannockburn 1314 - An excommunicated Robert the Bruce (for murder of a rival in a Church) leads Scots to their greatest ever victory.
5) Fornovo 1495 - Forces of the League of Venice organized by the Papacy against Charles VIII of France take on Franco-Swiss Army and get mangled in combat with the Swiss and French Gendarmes. Their greatest success was due to Greek-Albanian (non Catholic) Straidots who took the French baggage including all of their loot from Naples.
6) Ravenna 1512 - Papal Holy League against the French, a famously hard battle with very heavy losses on both sides including the French Commander while the Holy League lost 9,000 out of 16,000 and all its artillery.
7) Sack of Rome 1527 - Pope Clement forms the League of Cognac to oppose the domination of Italy by the Emperor Charles V (after his great victory over the French in 1525). Unpaid Spanish-Imperial Army looking for its wages and plunder march on Rome under fairly nominal command of a renegade Frenchman who gets killed in storm of Rome. Germans and Spanish then sack Rome while Pope Clement just gets into the Castel Sant'Anglo.
Charles V finally gets some cash to his Spanish Officers who bring Army back under control. Allowing Pope to surrender, agreeing to pay a huge ransom and cede substantial territory to Charles Kingdom of Naples. Charles probably was rather embassed by brutal conduct of his troops who included many Protestants in the German formations but actually the very Catholic Spanish were as bad if not worse than the German Landsknecht forces. But Charles happy to take advantage.
Thirty Year war - everyone seems to have totally ignored the Papal Bulls when making peace etc while French Cardinal Ministers spent a fortune backing the Swedes and other Protestant foes of their Catholic rivals and the Catholic League of German Princes which had tried to remain seperate from the Imperial Cause (with Papal support) was finally ground down by French attacks and diplomacy which aimed to seperate it from the Emperor.
Plenty of other historic examples of conflicts were "what should of happened according to Roman theoy" failed to happen in exactly that way. Even though plenty of other examples can be found of were the theory works. Much the same with Crusades against heretics and unbelievers, since while many great victories were won which you can say were inspired by Catholic religious zeal. How do you explain a almost equal number of defeats?
Also in the long period in the C14 & C15 were the Church and Europe was split between a Pope based in Avignon and one based in Rome I can find zero evidence of which Pope you backed having an effect on troop or country morale. Certainly nothing in the 100 years war or in Anglo-Scots battles of this period would seem to show this as a major influence.
Current split in G10 seems to be split between Spain, France, Flanders, Savoy, Milan, Papal Territory of Avignon & Gonoa who back Pope Leo XII while Pope Clement has backing of Austria, Poland, Portugal, Venice, Tuscany, Papal States and the German Catholic Princes. While Sardinia and Sicily would seem to be in process of being flipped over to backing Pope Leo XII.
Expect which Pope you back to have zero influence in game on the battlefield but rulers may think they are under pressure to try to end the split one way or another and their honour score may deflect their success or otherwise. So if the Emperor defeats France & Spain and re-unites Catholic Europe under a single Pope based in Rome I expect his people will even forgive the fact that he is a proven arsonist who tells total fibs about it and gets caught out, and he will be once again the most "honourable" leader in G10.
While if the King of Spain gets on his white horse, wraps himself in the banner of Saint James and picks up the sword of the Cid to restore good Pope Leo XII, free Rome and Naples from Austrian Captivity and save poor suffering French Catholics from rapine and plunder at the hands of the anti-Pope heretic mercenary troops. Well the Spanish population may even forget about his somewhat irregular claims to the throne of Spain.
After famine number four wonder if Portugal will decide that they are backing the wrong Pope? Also wonder if the Bishop-Princes of Italy and Germany will provide to have the same rock hard moral fibre and be as keen to be martyred for Pope Clement as his Swedes when the pressure comes on?
In G7 no one believes threats of King Carlos the Good concerning a gelding knife since Agema NPCs know they can call his bluff safe in the knowledge that his wife will never allow it and force him to pay them bribes. But are Princes of the Church going to be so keen to call the bluff of Forbin when soaked in top quality Austrian Lamp Oil (for that cleaner flame) and his first mate is getting the matches out? Or answer (red hot poker) pointed questions from the Spanish about do you know were out traitor bishop is? And have you ever employed or supplied Swedish Heretic Mercenary troops?
My basic theory of morale in Agema games is - do not worry about complex theological questions on the battle field! Just keep it simple, direct and brutal and keep hitting! Basically morale is to the physical as 3 is to 1 so even if not feeling very sure about things it is important to swash that buckle and show confidence. Since if German Princes think France or any other power for that matter is cowed by the Emperor all they are marching towards is a nice victory parade through the streets of Paris and to get to sign a nice treaty they will keep coming. But if they know they are marching into a blood bath and as soon as they cross that frontier their name goes on a black list of Jackels to be hunted down a nailed to the burning gates of their own Palace even if takes a decade they may get cold feet.