…Amicable relationships, if they did exist, does not make the two Churches to be in communion with each other. …
Everything you said is true, but it isn’t that simple. In Sicily and Calabria the Greek Church remained in communion with
both the Pope of Rome (whom they accepted as their local primate) and the Patriarch of Constantinople until the Council of Florence. For example, in the 14th century St. Bartholomew of Simeri took a pilgrimage to Constantinople to visit the Ecumenical Patriarch, who sent him to Mount Athos to reform a certain monastery (the
bios of St. Bartholomew is unclear as to which monastery). After a couple years, St. Bartholomew was convinced that he had done as much good as he could there, and he returned to Calabria to found his own monastery. Wishing it to be independent of the local Greek bishop, he went and got autonomy for the monastery from the Pope of Rome. In other words, he acted as if the schism didn’t exist.
In Venice, the Greek Church remained in communion with Rome through the 18th century. Nicolas Bulgaris is usually considered Orthodox - his Catechism is published by the Ecumenical Patriarchate - and yet that book is never once critical of the Latins, quotes several Popes and Cardinal Bona for justification of the legitimacy of using leavened bread for Consecration, and begins most chapters with quotations from “the Schoolmen” (always St. Thomas Aquinas). He lived in the same place at about the same time as St. Macarios of Corinth, who was certainly an Orthodox saint.
I have also read that the Church of Sinai remained in communion with Rome until the 1700s and several Russian metropolitans through the 19th century, though I cannot confirm or validate these claims.
On Mount Athos, a Benedictine monastery flourished through the 14th century when it died out. In 1213 while the “Crusaders” were despoiling Constantinople, a number of monasteries requested protection from Pope Innocent III, and the whole Holy Mountain became a fief of the Pope (without paying him any tithes, of course) for about a century.
The Bull of Union at the Council of Florence was signed by three Athonite abbots - Moses of the Great Lavra, Gerontios of Pantocrator, and Dorotheos of Vatopedi. In 1628 Father Ignatius of Vatopedi went to the Congregation of the Propagation of the Faith in Rome and declared that his monks were willing to embrace the Union of Florence; the profession of faith he made on behalf of them was kept secret for fear of the Turks.
Not long after in 1636 the Protaton Monastery opened up a school run by Roman Catholic priests. It closed when the priests died. And during the same century the Great Lavra even invited the Jesuits to open up a school and offered them a church and a plot of land, but for some reason the offer was left unrealized.
In a more recent era, my own former pastor as a Benedictine novice in his youth went to Athos with the blessing of his spiritual director, and was told by his new abbot (the holy Elder Aemilianos of Simonopetra, I believe) that “whatever you may come to believe while you are here, the Church of Rome is your mother and you must always love her”; he stayed there for twelve years. Orthodox students from Eastern Europe at my college will sometimes go to him or to a particularly holy and orthodox local Benedictine monk instead of the Orthodox churches nearby, and I have heard of other cases of Orthodox going to Eastern Catholic churches simply because they are looking for the best spiritual environment without particularly caring whether the church is in communion with Rome or not.
The well-known Jesuit theologian George Maloney (translator of St. Symeon the New Theologian, and author of a number of books including “The Mystic of Fire and Light: St. Symeon the New Theologian”, “A Theology of Uncreated Energies”, and “A History of Orthodox Theology Since 1453”) died being both a Jesuit and the pastor of a Russian Orthodox church. (Dominicans had also accepted Greek Orthodox bishops as their legitimate ordinaries after the 1054 schism, in their attempt to heal the situation.)
The Melkite Metropolitan Elias Zoghby proposed what came to be known as the “Zoghby Initiative”, by which they declare themselves in communion with both the Catholic and Orthodox Churches, holding the Orthodox Faith and all it teaches and accepting communion with the Bishop of Rome according to the authority he practiced in the 1st millennium. Hundreds if not thousands of faithful and parishes accepted this, though it received a notice from Cardinal Ratzinger in the CDF (for the following reasons: The Patriarch of Antioch is not willing to accept it, it can only be legimitate if by the “Orthodox Faith” they understand that it is the same as the Catholic Faith, and if by the role of the bishop of Rome in the 1st millennium they acknowledge it to be the same as the role of the Bishop of Rome today).
Finally, many Russian Old Believers claimed they had never left communion with Rome (calling themselves the “Old Catholics”), and Vladimir Soloviev was quite adamant that the Pope had authority over the Russian Orthodox Church, that he himself had not left the Russian Orthodox Church by professing personal communion with Rome, and that in practice most if not all Russians accepted the spiritual authority of the Pope.
St. Alexander Nevsky was also said to have been in communion with Rome, and St. Theophan the Recluse was received in a Papal audience (though this was in a diplomatic function).
Although they aren’t officially in communion with the other Orthodox or the Catholics, in practice in Eritrea people will alternately practice in either the Tehawedo Church or the Roman Catholic Church depending on where they feel like going that Sunday. I have an acquaintance who was raised in both.