From the text below, we learn that the process of the schism between the Catholics (known as "Latins" in the text) and the Orthodox (known as "Catholics" in the text) was a slow process. Though inter-communion had ceased sacramentally, the Orthodox allowed common prayer and the handing out of antidron to those schismatics who still maintained a certain level of Orthodoxy. It would be foolish to apply this text to our situation today, since the schism has taken its full effect, though I do believe some of the principles employed in the text can be considered to "the effect of gradually drawing them [the Catholics] over altogether to our [Orthodox] holy usages and doctrines."
Here follows an extract from the "Answers" of Demetrius Chromatenus, Archbishop of Bulgaria (A.D. 1203), to Constantine Cabasilas, Archbishop of Dyrrachium:
Question: Is it any harm for a Bishop to enter the churches of the Latins, and to worship in them, on any occasion when he may be invited by them? And should he give them the kataklaston [that is, the antidoron or blessed bread,] when they are present at the Liturgy in the Holy and Catholic [Orthodox] Church?
Answer: There are some of the Latins who do not at all differ from our customs either doctrinal or ecclesiastical, but are, as one may say, in this respect double-sided or neutral. As then it is our duty, and agreeable to piety, stiffly to oppose them that essentially differ from us, especially in the point of the doctrine of the Procession of the Holy Spirit, so on the other hand to use condescendence towards them that are not such, and to go with them into their churches, will be no fault in the Bishop who is charged with, and aims after, such economy as befits a steward of souls. Wherefore he will both go, when invited, to their churches without scruple, (for they too, no less than we ourselves, are venerators of the Holy Icons, and set them up in their churches) and will give them freely the Antidoron when they are present in the Catholic Church and come up to receive it. For this custom may have the effect of gradually drawing them over altogether to our holy usages and doctrines. Italy itself is thickly studded with churches of the Holy Apostles and Martyrs, the chief of which is the celebrated Church of Peter the Chief of the Apostles at Rome. Into these churches our people go freely, priests and laymen alike, and make their prayers to God, and render to the Saints who are honoured in them their due relative veneration and honour. And by doing this they incur no manner of blame, the churches in question being all under the Latins.
We remember that there were some Questions asked a good many years ago by Mark Patriarch of Alexandria, of blessed memory, and Answers written to the same by Theodore Balsamon, late Patriarch of Antioch. Among these there was one Question relating to Latin captives, namely, whether such ought to be admitted, when they come to the Catholic churches and seek to partake of the divine Mysteries? and subjoined to this an Answer altogether forbidding that the aforesaid Latins should be admitted to receive the divine Communion at the hands of our priests. The Answer professed to ground itself upon the Holy Scripture, and quoted that saying of the Lord: "He that is not with Me is against Me; and he that gathereth not with Me scattereth".
This Answer however was disapproved of by many of the most eminent men who were living at that time, as showing too great harshness and bitterness, and an unjustifiable tone, in blaming the Latin forms and customs; because all this, they said, has never been read or decreed synodically, nor have they ever been publicly rejected as heretics; but both eat with us, and pray with us. And any one, they said, may readily prove the justness of this reasoning from Canon XV of the Holy Synod which is called the First and Second of Constantinople. And again because this very fact of the Latins coming to us, and seeking to communicate at our hands of the Holy Oblation which is made with leavened bread, shows plainly that they cannot think much of their Azymes, nor make any great point of sticking to them: else they would not come to our celebration of the Divine Mysteries. These too, in order to support their own view from the Gospel, alleged what was said by St. John to the Lord. "We saw," he said, "'one casting out devils in Thy name, and we forbade him, because he followeth not with us. And Jesus said unto him, 'Forbid him not, for whosoever is not against us is for us.'"
They urged also in addition that the words "He that is not with Me is against Me" are plainly and exclusively intended by our Saviour for the devil, as the context of the Gospel in the same place shows. For as Satan is an enemy from the beginning, and abides unchangeable in his malice, and is absolutely incapable of repentance, in this sense he, not being with the Lord, is against Him, and from so being has his name Satan, or adversary: inasmuch as the Lord loveth His own creation and gathereth it to Himself, but Satan hateth it and scattereth. But the words "He who is not against us is for us" are spoken in reference to a man who, though he follows not Jesus, yet emulates them that do follow Him, and in His name casts out devils, and so from walking apart may easily change to following. For mere human infirmity there is a remedy, namely, conversion and repentance, and to change from what is worse to what is better.
They appealed also to the judgment on this same subject of Theophylact, the most wise Archbishop of Bulgaria,…which discourses of condescension and economy in a manner worthy both of admiration and of praise. And so they who argued against the opinion of Balsamon, as has been related, were judged to have insisted piously and reasonably for giving the preference over inflexible harshness to economy, in order that so, instead of casting down, we may gently and gradually win our brethren, for whom our common Saviour and Lord shed His own most precious blood.
As quoted in William Palmer’s Dissertations on Subjects Relating to the ‘Orthodox’ or ‘Eastern Catholic’ Communion (1853).