No, the Eastern Orthodox Church was NOT involved in any massacres or genocide of others because of their religion.
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There is a lot that can be misunderstood or completely missed when it comes to the "History of the Church" unless one has studied it for years.
The Eastern Orthodox Church, the church that was literally started by the REAL Apostles of Jesus, along with the Church in Egypt, Syriac Orthodox, Coptic Orthodox, Ethiopian Orthodox, Eritrean Orthodox, Malankara Orthodox Syrian Church (India), Persian Church, and Armenian Apostolic churches began having MAJOR problems with the Roman Church as early as the First Council of Nicaea in 325. ..... as opposed to the Church of Rome that was started by a foreign Jew,Paul, from what is today, Northern Turkey..... who had a "vision".
This was during a period where there were no less than 200 Christian Churches.
It was the Greek and Egyptian Orthodox Church groups that were the oldest, truer Christian churches having been established along with the other "closer to Jerusalem" churches by the 12 Apostles and close disciples of PHYSICAL Jesus.
The Church of Rome had its OWN agenda from the very beginning, going as far as Paul selecting his OWN Pope over the Pope selected by the REAL Apostle of Jesus, Peter, "the Rock of the Church", at the Jerusalem Christian Church.
There is absolutely NO substantiated evidence the two men ever even met.
The rift continued to grow between the East and Roman churches.
The opulence and luxury of Rome was becoming quite a concern, let alone their dogma, ideology, organization, but especially its authoritative nature.
In 451 the Church in Egypt SPLIT off into two different groups.
After the Fall of Rome in 476, the Greek Church peacefully integrated into the Byzantine Empire, which succeeded in doing nothing but ticking off Rome.
Some of the Greek Church along with some of the Roman Church integrated TOO well, making the rift even larger.
The third bunch was not as historically defined though quite noticeable, and that was the "Christian Church of Constantine" or rather "church opportunists" who went where the money and power was.
Constantine had his own agenda - an agenda the Romans slowly picked up on.
The Crusades belonged to the Roman Church.
This was the Roman Church's way of getting rid of "undesirables", whether Pagan, Muslim OR Christian at the end of the sword.
The Roman Church's Crusaders sacking of Constantinople, the sacking of Church of Holy Wisdom and establishment of the Latin Empire as a seeming attempt to supplant the Orthodox Byzantine Empire, the murder of priests, the torture and murder of over 7000 Christian Cathars, the murders of many other small Christian sects ..... the SPLIT was bound to happen.
The Eastern Orthodox Church did not have a military aspect to it like the Roman Church and had a high tolerance of other Christian Churches though they believed all groups outside of the Orthodox Church are not seen as being members of the Church proper, but rather separated brethren who have failed to retain the fullness of the Christian faith and theology, as was given to the apostles by Jesus Christ.
Sure there were individuals that switched sides or played the field but do not confuse even the earliest Eastern Orthodox Church with the Roman Christian (Catholic) Church.
They have NEVER been the same church.
First of all, let me stress that even if the population of "just" a small village is exterminated, one can speak of a massacre, isn't it!?!
Then, to my understanding, the point of your question is whether the Eastern Orthodox Church organized any systematic war against enemies of the true faith and in the name of that faith during its course of existence.
And so, now to attempt to answer that point:
THE Crusades - the ones western historiography writes about - were indeed an outcome of the Western (European) Christian zeal. Nevertheless, Alexios Komnenos, the Byzantine Emperor at the time of the First Crusade, had contacts and "contracts" with the crusaders.
These crusaders were attacking the regions where the Eastern Orthodox Church had its heartlands. That we mainly commemorate only the 1204 sacking of Constantinople by the Fourth Crusade is just because of the highly dramatic (call it even tragic...) character of the event.
I'd say that the Eastern Orthodox Church was more active in a violent way to big masses of populations during the Christianization period, and during the fight against the various "heretics" (Arians, Nestorians, Mono- or Mia-physiques etc.). But were those really crusades!?!
Unless, you'd like to see post Medieval wars waged against the Ottomans by the Orthodox (be them Russians earlier or Greeks later) as "Crusades" (but to the appropriateness of such a characterization most would raise rightful, I believe, doubts), I'd say that the answer to your question should be rather negative...
I fully agree with Alexandros.
Please don't forget: the entire conflict was located inside the territory of the Byzantine Empire. Or what was left of it, anyway. They had seen their empire eaten up, bit by bit, by Mohammedans. Who commit any kind of atrocity to expand their territory and promote their fate. Surely you realize that only Jesus Christ himself turns the other cheek, and then not always. To imagine that the EO Church would never ever respond in kind is rather naive, to say the very least.
Of course there have been atrocities committed by the Eastern Orthodox Church. Compared to their competitor, the RC Church, they were much better equipped for it. The EO Church was a state church. The RC Church never was the official state church of any country. (Of course, the RC Church found they ranked above mere countries.)
I cannot give you an example, as I haven't studied the crusades and the reason why it began in detail. But you can rest assured that the EO Church has their own fair chair of skeletons in the cupboard. All monotheistic religions have, they are not an exception.
No
The Byzantine Empire was the main Orthodox power base and was on the defense pretty much from the dawn of Islam.
Altho Emperor Alexius called the pope for help against Turks he meant soldiers not an angry mob of religious fanatics supported with chivalric knights and monks.
Despite that it was still favorable for the Byzantines as the Crusaders took many important cities and defeated several Arab armies.