As far as the Crusades go, the fourth Crusade was a real disaster with Bishops from Venice praying for the destruction of the Greek Orthodox. I suppose we could go into the many horror stories associated with that Crusade, such as the brutal rape of Greek Orthodox nuns who had dedicated their lives to Christ. And the fact that much of the incredibly valuable loot stolen from the Greek Orthodox Churches found its way into Roman Catholic Churches in the west and was never returned.
We could also go into the history of the Fourth Crusade a bit deeper. It started out innocently enough. The fighters were largely Franks. They set out for Venice, where they thought they had passage arranged with Venice. In the meanwhile, they were approached by the son of the deposed emperor of Byzantium, Isaac Angelus, who promised to pay their passage to Palestine and also provide 10,000 Byzantine soldiers to the effort IF they would reinstate his father on the throne. They agreed to that. In another subcurrent, the Venetian fleet was actually controlled by the Venetian ruler, Enrico Dandolo. Dandolo had been blinded or partially blinded by the then ruler of the Byzantine empire in a persecution/purge of Italians in Constantinople. (maybe the Greeks had good reason and maybe didn’t) Dandolo upped the cost of passage, wouldn’t rely on the Byzantine promise and added the further condition that the crusaders also take the Adriatic city of Zara, which had recently shaken off Venetian domination. So, the Franks agreed to that as well.
The Pope threatened excommunication on all crusaders who would war against Christians. They took Zara for Dandolo and were excommunicated for it. Then off to Constantinople, even so.
The Byzantines at first agreed to reinstate Isaac Angelus, but then refused and deposed him again when they heard the full terms. One of the further conditions promised by Isaac Angelus’ son was that the Orthodox would reunite with the Latin Church; a promise that was unacceptable to the powers that were in Constantinople.
So, everybody got angry with everybody else. The Byzantines deposed Isaac Angelus again, closed the gates on the Franks, leaving them to starve into submission outside the city. But the former made a terrible mistake in additionally sallying out to drive the Franks away. The Franks were outnumbered but were by far the better fighters and took the city. And, indeed, they did sack it. Never did get to the Holy Land. Some of the Frankish leaders decided to stay and rule the city, which didn’t work out. The rest drifted home, and a fair amount of loot did make its way back to the west with them. Some of it was even given to various Latin churches, the bronze horses atop St. Mark’s in Venice being an example, compliments of Enrico Dandolo. They had been taken from a horseracing arena in Constantinople.
About 250 years later, the Turks conquered Constantinople. Some Orthodox blame the Latins for that, asserting that it weakened Constantinople’s resistance. And it might have.
On the other hand, one has to wonder whether a city that was conquered by 8000 Franks without cannon could have resisted assault by 200,000 Turks with cannon, no matter what. The Kingdom of Hungary did try to assist Constaninople, but got conquered by the Turks itself for its effort. Later, of course, the Turks very nearly took Vienna, and probably would have but for Jan Sobieski and his Polish cavalry.
But it’s all still a contentious thing, and draws debate. The one sure thing about it is that it’s not as simple a case as many claim it is.