This is true - that the Church is the Body of Christ is an essential part of the Orthodox doctrine. We are grafted onto that Body as a result of our faith, and for us, the sacrament of Baptism is the means by which we believe our union with the Body of Christ is completed. And we call the Eucharist, the Lord’s Supper, Holy Communion, because in the Eucharist we are in communion with the entire Body of Christ.
This is also why
@Hentenza the Orthodox do not admit anyone to the Eucharist - because while we know where the Body of Christ is, we do not know where it is not, and because if we allowed someone who might not be a member of the Body of Christ to partake, it could harm them and we would be held accountable, as I explained to you before. Once we know a person or church is part of the Body of Christ, then reception of the Eucharist becomes possible.
For example, there was a long schism between the Eastern Orthodox and the Oriental Orthodox, with the EO accusing the OO of monophysitism, and the OOs accusing the EO of Nestorianism. Both were in error, and came to recognize this at times, and there were periods of close cooperation. We venerate some people who were definitely Oriental Orthodox as saints, such as St. Theodora, and likewise we venerate a member of the Church of the East, St. Isaac the Syrian, which is a group that at one time was Nestorian but by the time of St. Isaac no longer used his flawed Christology. Thus, the rule has normally been, according to our canons, even when we were not sure of the status of those churches, that their members could be received by confession rather than chrismation or baptism (Roman Catholics and Protestants are usually chrismated, with some exceptions which I will mention).
However at other times our shared faith has been recognized. There were periods of communion with OO churches in the past, and at present this is on an unprecedented scale - in 1991 the Antiochian Orthodox and Syriac Orthodox, the main EO and OO jurisdictions in Syria, Iraq, India, Turkey (the eastern part only in the case of Antiochians for the western part is under Constantinople) Lebanon and Iran (most Antiochians are in Syria and Lebanon only these days, along with emigres who live in Qatar, cities in the United Arab Emirates like Dubai and Abu Dhabi, and also Kuwait, Bahrain and Oman, that is to say, those Gulf States which are tolerant of Christians, unlike the Saudis or Yemenis, whereas the Syriac Orthodox have indigenous populations throughout the entire region and also are present in Jerusalem and Bethlehem at the Holy Sepulchre and the other major sites of pilgrimage, ahd the most likely location of the Cenacle is a Syriac Orthodox monastery*. These two churches recognized each other’s Orthodoxy and entered into a relationship where members of either church can receive the Eucharist in the other, marry members of the other, and indeed one cannot, in the Middle East, convert between the two churches, since this would violate the principle of trust by encouraging a situation where one began to try to encroach upon the other. A similar agreement was then achieved between the Coptic Orthodox Christians of Egypt and the Alexandrian Greek Orthodox.
But even outside of this there have been examples of recognition, now that the knowledge of Oriental Orthodox orthodoxy exists - for example, St. Catharine’s Monastery in Sinai is known for giving the Eucharist to Coptic Orthodox pilgrims, all the major Eastern Orthodox churches had memorial services in 2015 for the victims of the Armenian Genocide (which was the largest in terms of victims of three concurrent genocides launched by the Turks against Christians, the other victims being the Suroye, the ethnic group of the Syriac Orthodox and the Church of the East, also known as Assyrians or Aramaeans or Chaldeans, and the Pontic Greeks. Of the three, the Armenians suffered the highest number of casualties, the Suroye suffered the highest percentage loss of their population, and the Pontic Greeks, due to a population exchange with Greece in which Turkey forced Greece to deport its Muslims to Turkey and in return the Turks would permit the Greeks to leave their ancestral homelands in Asia Minor for the western half of the central region of historic Greek lands under the Kingdom of Greece, were the most completely eradicated from Turkey, in that there are almost no Greek Orthodox churches outside of those in Istanbul in the Phanar (the Phanariot Greeks were allowed to remain, because Turkey recognized the geopolitical benefits of being the country that was home to the Ecumenical Patriarchate of Constantinople, the seniormost Orthodox bishop, whose Patriarch does not include all of Greece but does include all areas not under the Archbishop of Athens, that is to say, those lands added to the Kingdom of Greece after the 1812 revolution, for example, Thessaloniki, Crete and most of the Greek islands, and also most importantly, Mount Athos.
Indeed even ROCOR, known for being one of the most traditional Orthodox denominations, is known for having given the Eucharist to Copts in Canada in the 2000s while the Copts in that city were working to organize a parish of their own. Likewise ROCOR recognized some Anglican priests, and received them without requiring them to be Chrismated and re-ordained, a process known as Vesting, which normally only happened to Roman Catholic clergy wishing to convert, and at that, mainly to Eastern Catholic clergy (and also of course to clergy from the OO and Assyrian churches).
Unfortunately, there are those opposed to the reunion between the OO and the EO, just as there are those who want us to have nothing to do with Roman Catholics (and on the other side also). The Old Calendarists, a schismatic group, tries to promote the idea that the Orthodox should not attempt to unite other Christians with us through ecumenical dialogue, by falsely claiming that ecumenical reconciliation is inherently syncretic (this is not the case - with regards to the OO it was realized their faith was the same as ours, and indeed substantial parts of the EO liturgy were written by Oriental Orthodox, such as the hymn Ho Monogenes, and conversely, many parts of the OO liturgy are of EO origin, having been written by St. Romanos the Melodist and St. John of Damascus. And both churches share large parts of the liturgy which either predate the schism or which do not, but no one knows who wrote it, for example, Holy Unction, tne liturgy for consecrating oil for the annointing of the sick and the fasting (which is also used as a blessing for those who are sick).
This is my favorite liturgy in fact, because i love its structure: it consists of seven, or in the case of the Syriac Orthodox, five, sets of prayers and Scripture lessons, each section having an Epistle and a Gospel, and there are Psalms included and typically after each prayer one of five or seven lamps set out in the shape of a cross containing the oil being consecrated, or a wick into one bowl containing all of the oil being consecrated, is lit. Additionally we will do this liturgy with seven Presbyters. Insofar as the use of oil to annoint the sick and the fasting is directed in the Epistle of James and the Gospels directly, this is a service that is scripturally uimpeachable, and also lacks the characteristics of the Extreme Unction service that troubled Martin Luther (and I would note that St. James did not say only the dying should be annointed with oil, but that was at the time the practice in the Western church, but since then Rome and the Protestants have greatly improved their services for unction, but I still prefer the Eastern and Oriental Orthodox form of the liturgy.
*On this point other location favored by the Crusaders, which is home to a ruined Gothic church, I strongly believe is the Tomb of David, so I agree with the Jews in that respect; the Muslim claim to it is invalid - there should be a church there since Christ is the Root of Jesse, directly descended from St. David the King, Prophet and Psalmist and his son St. Solomon, on the side of His mother obviously, since on His fathers side he is descended from no one, for God the Father is unoriginate, and Christ is begotten of Him before all ages, begotten, not made, and of one essence with His Father and with God the Holy Spirit; very God of very God, who became Man for our salvation. Thus I favor restoring the gothic church but as a church dedicated to St. David. But there is no reason not to allow the Jews to pray in our churches dedicated to those who they also venerate, and indeed it might move those who have not already embraced Christ to do so (the Syriac Orthodox and Antiochian Orthodox are largely of Jewish descent, in both India and the Middle East, the Mar Thoma Christians in India being descended both from the Kochin Jews who settled in Malankara in the 2nd century BC, and converts from Hindu paganism. Indeed St. Thomas the Apostle received the crown of martyrdom in 53 AD when the enraged Maharajah of Kerala threw a javelin at him. The Ethiopians and Eritreans, also Oriental Orthodox, are almost entirely descended at least in part from Jews, from the Beta Israel, and there are still around 3,000 Jews in Ethiopia, the rest having migrated to Israel in the 1970s after Emperor Haile Selassie was martyred by the Derg communist regime for refusing to denounce the Christian religion - for this he was strangled. Thus the Ethiopians are among those Christians blessed to have received crowns of martyrdom for confessing Christ to both Communists and Muslims, which also include the Albanians, Hungarians, Carpatho-Rusyns, Moldovans, Russians, Ukrainians, Romanians, Bulgarians, Serbians, Macedonians, Croatians, Slovenians, Montenegrins, all of whom were ruled by the Turks or in the case of parts of Russia and Ukraine, by Muslim hordes for a brief period, particularly in Ukraine, and in the case of Russia also by those in Checnya and Dagestan, and the Armenians and Georgians.