Here is some thought on the reason that may lead to the imbalance of accepting Holy Communion between the Catholics and Orthodox today. This is from a Catholic convert, thus it may be from one side of the story. Perhaps we can have some thought from the Orthodox too, if possible.
One reason for Orthodoxy’s attractiveness back then was simply that, for me, its image remained refreshingly untainted by the emotional anti-Catholic Calvinist prejudices which I had imbibed against “Romanism” during adolescence. Nobody, as far as I knew, was describing Istanbul as “Mystery Babylon.”
I was running up against the rather obvious fact that Orthodoxy is, well, not exactly catholic. It lacks the cultural universality and openness, the capacity to provide a true and welcoming home for all the world’s tribes and nations, that is in fact one of the four marks of the true Church: one, holy, catholic, and apostolic. Every word of the liturgies I attended in Sydney—including the Scripture readings and preaching—was in Greek, of which I understood absolutely nothing. The thesis that Eastern Orthodoxy is the true religion was turning out to bear the practical corollary that, to share fully and fruitfully in the life of the Body of Christ, one would almost have to become a Greek. (Well, O.K., maybe a Russian, a Serb, a Syrian—but in any case the ethnic options would be very limited.)
Does Orthodoxy Make Sense?
In short, Eastern Orthodoxy, as far as I could see at that stage of my journey, had certain strengths over against Catholicism, but also certain weaknesses.
In this case the debate was mainly over the nature of the Petrine primacy,
if God has given the gift of infallibility to his Church, there must be some identifiable authority or agent within her capable of exercising that gift. Now, Catholics believe that the College of Bishops—the successors of the apostles, led by the pope, the successor of St. Peter—constitute that authority.
they (the Orthodox) recognize as ecumenical only the first seven councils: those that took place in the first Christian millennium, before the rupture between East and West. Indeed, even though they claim theirs is the true church, since that medieval split they have never attempted to convoke and celebrate any ecumenical council of their own. For they still recognize as a valid part of ancient tradition the role of the See of Peter as enjoying a certain primacy—at least of honor or precedence—over the other ancient centers of Christianity (Constantinople, Antioch, Jerusalem, and Alexandria).
Thus, mainstream Orthodox theologians, as I understand them, would say that for a thousand years we have had a situation of interrupted infallibility. The interruption, they would maintain, has been caused above all by the “ambition,” “intransigence” or " hubris" of the bishops of the See of Peter, who are said to have overstepped the due limits of the modest primacy bestowed on them by Jesus. However (it is said), once the Roman pontiffs come to recognize this grave error and renounce their claims to personal infallibility and universal jurisdiction over all Christians, why, then the deplorable schism will at last be healed! The whole Church, with due representation for both East and West, will once again be able to hold infallible ecumenical councils.
After the East-West rupture that hardened as a result of the mutual excommunications of 1054 and the brutal sack of Constantinople by Latin crusaders in 1204, two ecumenical councils were convoked by Rome for the purpose of healing the breach. They were held at Lyons in 1274 and at Florence in 1439, with Eastern Christendom being duly represented at both councils by bishops and theologians sent from Constantinople. And in both cases these representatives ended up fully accepting, on behalf of the Eastern Church, the decrees, promulgated by these councils, that professed the true, divinely ordained jurisdiction of the successors of Peter over the universal Church of Christ—something much more than a mere primacy of honor. And these decrees were of course confirmed by the then-reigning popes.
Why, then, did neither of these two councils effectively put an end to the tragic and long-standing schism? Basically because the Eastern delegations to Lyons and Florence, upon returning to their own constituency, were unable to make the newly decreed union take practical effect. At Constantinople, the nerve-center of the Byzantine Empire, an attitude of deep suspicion and even passionate hostility toward the Latin “enemies” was still strongly ingrained in the hearts and minds of many citizens—great and small alike. The result was that politics and public opinion trumped the conciliar agreements. The Eastern Christians as a whole simply refused to acquiesce in the idea of allowing that man—the widely feared and detested bishop of Rome—to hold any kind of real jurisdiction over their spiritual and ecclesiastical affairs.
catholic.com/magazine/articles/why-i-didn%E2%80%99t-convert-to-eastern-orthodoxy