Another demonstration of Realpolitik comes from examining the claims of those who talk about a Muslim-Christian culture war. Such a culture war exists only to the extent that it serves the agenda of those who claim the culture war's existence.
Consider the Coalition from the First Gulf War - USA, UK, Saudi Arabia, Kuwait, Syria, etc etc. Plenty of Muslim countries which saw their interests better served by aligning themselves with the Crusaders than with their fellow Muslims.
During World War One, Germany and Austria-Hungary had no problems aligning themselves with Ottoman Turkey, and religious figures in Turkey had no problems calling down a fatwa on some Christians - that is, the UK, Russia and France.
And about 60 years earlier those same Brits and Frogs had been Ottoman allies in the fight against Russia - because once again geopolitics was far more important than religion.
In fact throughout history it's easy to find examples where Christians and Muslims found geopolitics trumped religion, such as in the 16th century when France was surrounded by the politically and religiously aligned Spanish and German Empires, so the King of France made an alliance with Suleiman the Magnificent of Turkey.
But the best examples come from the Crusades. Anyone who thinks the Crusades were solely about Christians fighting Muslims knows nothing about the Crusades.
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1. The origin of the Crusades lay in a religious dispute, but not one involving Christians. In the early 11th century the Seljuk Turks, then located in Central Asia, converted to Sunni Islam, and then vowed to unite the whole Islamic world for the (then powerless) Caliph in Baghdad. This meant conquering the Shia Fatimids of Egypt and their heretic Caliph in Cairo. On the way to Egypt some loosely allied Turkoman tribes decided on a bit of freelance raiding of the Byzantine Empire. The Emperor responded and his army was soundly defeated. The Turkish tribes occupied most of Asia Minor (that is, what's now Asian Turkey). Twenty years later another Byzantine Emperor, Alexius, asked for assistance from Western European leaders. He was looking for mercenaries. What he got was the First Crusade.
2. The Pope's model for organising the Crusade was the Norman invasion of England 30 years earlier, to the extent of formally blessing the standards of the commanders. Yes, back in 1066 the Pope at the time had formally endorsed Duke William's invasion because at the time the English church was considered to be heretical. Thus William's invasion had, among other objectives, the very religious objective of rescuing the English church from heresy. Much the same formulation was followed for the First Crusade.
3. The first target of the Crusaders was the city of Nicaea. However the Crusaders had little knowledge of siege warfare and Nicaea had high stone walls. Emperor Alexius soon turned up with a siege train, and the Byzantine siege engines knocked down a section of wall. The Crusaders informed Alexius they were going to attack the city the next morning, but the next morning they were astonished to discover Byzantine flags flying from the city's towers. Overnight Alexius had convinced the Turkish garrison to surrender and leave the city. The Crusaders were furious that Alexius had effectively stolen the city from under their noses, firstly because it now meant they wouldn't be able to sack the city, and secondly because the Turks were allowed to live and might fight them again in the future. But Nicaea's population was still overwhelmingly Greek and Christian and Alexius wanted the city back intact. He paid off the Crusaders with a large pile of gold - still cheaper than rebuilding a destroyed city.
4. During the march to Antioch, the Crusaders received an embassy from some Muslims who were seeking an alliance. Given that they saw their job as killing Muslims, the Crusaders dismissed the embassy. It turned out the embassy was from the Fatimids, who were just about holding the Seljuks at bay on the border of Egypt, and who saw the Crusaders as a useful ally in what they (the Fatimids) thought was a war against a common enemy.
5. After capturing Antioch (after a siege lasting more than a year), the Crusaders had to turn around and face a large Turkish army, consisting mostly of cavalry. But the Crusaders had lost so many horses to starvation that their army was now mostly infantry. Yet despite being hungry, outnumbered and mostly on foot, the Crusaders were victorious. No wonder the victory was seen as a miracle. But what the Crusaders didn't realise was that the Turkish tribal leaders saw their own commander as more of a threat to their independence than this Christian army and abandoned him, leaving him to fight the battle with only his own retinue. No surprise then that he was defeated.
6. The Crusaders, now full of religious fervour from their 'miraculous' victory, marched on to Jerusalem, which they captured. What they didn't realise was that the garrison was actually Fatimid, not Turkish. The Crusaders were so unaware of Muslim politics that in marching from Antioch to Jerusalem they didn't notice they'd crossed the front line of a completely separate religious war.
7. The First Crusade created a power vacuum in the Middle East. The Crusader princes immediately fell to arguing and fighting among themselves, and all sides soon realised the benefits to be gained by forming alliances with local Muslim tribal leaders, who were just as fractured among themselves as the Crusaders were. Within 10 years of the Crusader capture of Jerusalem we have records of battles in which both armies consisted of Crusaders and Muslims.
Now in the end the Crusaders lost their last cities to a united Muslim state (the Mamluk Sultanate), but this Muslim unity was the exception rather than the rule. The main reason the Crusader states lasted nearly two centuries was because for most of that time the Muslims of the region were divided among themselves, and saw the Crusaders as useful allies rather than a religious enemy.