Ecumenical theology owes its origins to the Magisterial interventions of an occupant of the Petrine See of Rome. It began early in the first millennium with the Western Church setting itself free from the 'common sense' proposition that, since the Spirit is the possession of the Church, the Sacraments (fruits of the Spirit) cannot exist outside that Church.
Common Sense is, so very often, a dangerous superstition. (Another example of this is the conviction of worthy but confused people that a pope who teaches error cannot truly be a pope.)
Pope S Stephen I (pope 254-257) opposed such a Common Sense view, insisting that heretical baptism is valid. Augustine, during the Donatist controversy, established that Holy Order could validly exist among schismatics.
In times of controversy there is always a temptation to think that one's opponents, so grave are their errors, cannot possibly be validly conveying sacramental grace. (In our own time, the Sedes, poor poppets, are tempted by this 'certainty'.) But inexorably there grew up in the West the conviction that a valid minister with a very minimal intention and using an adequate Form and Matter could validly convey the sacraments, even when in a state of mortal sin, even when in schism, even when in heresy, even if apostate.
The ultimate and sure basis for such a view lies in the certainty that the Lord Himself is the source of the sacraments and that He Himself guarantees them and that His word is Truth.
Sometimes silly people dismiss talk about validity and invalidity as 'rigid' and 'legalistic' and 'mechanical'. Foolishly, because they do not realise that the only alternative is the 'Cyprianic' view: that anybody who is not within (what the speaker confidently defines as) "the Church", lacks Baptism and all the other sacraments. This is a view that has been held in the Orthodox Church; Timothy Ware aka Metropolitan Kallistos once observed that while Westerners did not often, for obvious reasons, meet such Orthodox, they should not forget that they exist.
Indeed they do; a very fine Orthodox piece of theological exegesis emerged in 2014 (Greek edition; English translation in 2015) which sought to demolish the entire tradition which descends from Pope Stephen through S Augustine and S Thomas Aquinas down to the 'One Baptism Ecumenism' of Vatican II. Called The Ecclesiological Renovation of Vatican II, by protopresbyter Peter Heers, it demonstrates with great clarity where you get to if you reject the Magisterium of Pope S Stephen I. It shows that 'Vatican II' is very far from being some sort of henotikon which all Orthodox are rushing with grateful hearts to embrace. But Vatican II is right and Heers is wrong.
Confusion also involves the Sacrament/Mystery of Holy Order. Last year, a Ukrainian Catholic Priest called James Siemens, a Canadian ex-Anglican, sadly joined one of the Orthodox jurisdictions which have been involved in the ructions between Constantinople and Moskow, and was received as priest, that is, without reordination. This has caused no little dissension on the Orthodoxosphere.
So it is clear that not all Orthodox necessarily accept exactly the same reading of the same data. A friend of mine, baptised as a presbyterian, became Orthodox in Brighton simply by being chrismated. When he subsequently became a monk on Mount Athos, this was all deemed a nullity and he was baptised and chrismated afresh. Yet both Mount Athos, and Holy Trinity Brighton ... so gaily painted in the Greek national colours of white and blue! ... acknowledge the primacy of the 'See of S Andrew'.
Such a praxis implies, of course, that all non-Orthodox are unbaptised heathen. For Orthodox with these attitudes, PF is not only not any sort of Sovereign Pontiff; he is not a Bishop, not a priest, because he is not even a baptised Christian layman.
There is, surely, little possibility of 'ecumenism' with those who are entangled in the enchanting locks of this particular Neaera. I am not sure how wise it is for some Westerners to feel that 'Unity' with the Separated Byzantines is so much simpler a proposition than Unity with Rome.
Only the 'mechanical' and 'rigid' and 'legalistic' papal teaching, that valid sacraments can exist outside the canonical bounds of the Church, affords a basis, both theologically and practically, for ecumenical activity and progress. Vide Communionis notio and Dominus Iesus.
It is to be applauded and embraced.