How could Orthodoxy have existed in pockets of Western Europe? From what I understand, though there were bitter theological differences between East and West, and political rivalries that most dramatically culminated in the Sacking of Constantinople, there wasn't the sort of internecine bloodshed and persecution between adherents of the two churches like there was between Protestants and Catholics. Or was there?
Before 700's, the two churches were kind of close, thanks to the Pope that mamanged to influenced a lot the west while being part of Byzantine policies. When Arabo-Islamic empire cut the connexions up to IX century, the distinction was made between kingdoms : you had the Iberic church with the visigothic king as its head, the Northern Italian (Ambrosian or not) with the Lombard king, the Frankish churches with the majordomo, etc.
It's both the cut and the rise of the Franks as the only christian power in West that changed things : critically with Charlemagne, standardizing the rites and the beliefs in all West really catalyzed the Catholic church against an Orthodox church that was in crisis (iconoclasm, among other things).
But the differences were still massively politicals, and the removal of orthodox priest from Southern Italy are more about the Normans than the power of the pope. And you had monasteries of italo-byzantine tradition up to quite late in Middle-Ages.
The main orthodox group was southern Italy, periodically revitalized by immigration coming from Balkans up to 1500's (Greek, Albanians, Slavs from Adriatic).
Of course, you had tensions, but it was more Lutherans/Calvinist scale than bloodshed.
In fact, you had really a cut appearing during Crusades : the latins were in direct contact with Byzance for the first time since the 750's and, as all groups evolving separatly, they had trouble to recognize each other.
If you add the fact the orthodox church was only a part of the Byzantine policy, not really the autnonmous (or even independent) organisation the Catholic church was...Let's say the Orthodoxs often payed the lack of support of Byzance towards the Crusaders by being less well treated than other oriental churches.
Finally, between 1100's and 1200's, the situation was really tense and eventually came to sack of Constantinople, that was almost a spontaneous reaction after years of provocations and not really kind events from both sides. But, and I insist, it was condamned by Papacy until they said themselves "Ok, what is done is done, so better to organize this better, and try to avoid the mess Holy Land is now".
Surprisingly, even after the recapture of Constantinople by Byzantines, things tended to go better, slightly, between the head of both churches (Pope and Basileus), but now the orthodox clergy was even more hostile to Latins.
And for the theological differences...As it was the case everywhere since the 700 in all Europe, every national church have its particular rites and differences.
To make a comparison, let's say that knowing these differences and appreciate their importance, was in the same scale than knowing every trotskyist organisation in USA and class them regarding political differences.
So hard and so pointless that is comical : the only difference of relative importance was the Filioque dispute. Franlky, some orientel churches joined the Catholics with more differences than that.
There probably wasn't too much interaction between the two churches in the Middle Ages anyway,
Southern Italy, Dalmatia, Croats/Serbs, Palestine, Southern Spain, pick your choice.
Frankish imperialism in Anatolia aside.
Frankish Imperialism? So, I suppose the kings of the Franks became King of Jerusalem, and that the policy of Latin States was fitting only Frankish interests?
More seriously, no. 5 states with nothing in common but being "Latins"...wait no, one was armenian. Okay, nothing in common but being "Frank...", damn, one was occitan, other armenian.
All were catholic maybe? Nuh.
Back on Earth : it was comparable to Arabo-Islamic invasions : a group of warriors with their clientele take a region and claim it as his own. The King of the Franks have little to say regarding that, and the ones that benefited for this were the conquerors and the settlers.
So how could there be significant minorities, or at least notable communities, of Eastern Orthodox believers in western Europe during the Middle Ages?
You had, in Southern Italy with remaining of old Italo-Byzantines, Greek and Albanians refugees...
Certainly there were Catholics going east for trade or crusade, but what could lead the Orthodox to go west?
Trade, but also, if you don't have the cut of 700's, Italy.
Let's take that Pope doesn't renounce Byzantine alliance to prefer Franks to help him against Lombards : Italy could have sided Orthodox.
Of course, it would have meant thaat the Basileus should have sawn an interest to this, because so far he was concerned it wasn't vital for the Empire. And there's what refrained Orthodoxy to expand : when it wasn't vital for the Empire.
On the other hand, Catholicism managed to be an unifing factor of west, with a certain autonomy from secular powers and with its own interests.