A friend of mine at Lancing, a presbyterian in origin, became Orthodox. At the Church of the Holy Trinity in Brighton (a church under the jurisdiction of the Ecumenical Patriarch), he was Chrismated (his presbyterian baptism, by implication, being deemed adequate). It was a very great and happy day, at which I was privileged to be welcomed.
Later, my friend discerned a vocation to the life of a monk on the Holy Mountain. There, in another part of the jurisdiction of the Ecumenical Patriarch, he was required to be baptised and chrismated de novo.
There are several cumulative implications here. Firstly, that on Athos it was deemed that he had previously been, in effect, an unbaptised non-Christian, outside the Ark of Salvation. I am reminded of an Orthodox community I know in England which appears to take this view and to emphasise that the 'Pope' is not 'the canonical bishop of Rome'. Yes, I am aware that at high levels, for example in the diplomatic-liturgical relationships between the Vatican and the Phanar, the plain meaning of the rituals (for example, on the feasts of S Peter and S Andrew) is that Benedict is Bishop of Rome and Bartholomew is Bishop of Constantinople. But on Athos, no insignificant part of Bartholomew's jurisdiction, a different ecclesiology apparently holds sway.
This is no small matter. The starting point of all ecumenism is the recognition of Christ in the baptised fellow-Christian. I know that some Roman Catholics are very pleased to feel certain that I am not a priest. I find this made easier to bear by the knowledge that some Orthodox do not think that I am even a Christian.
I think Byzantine Orthodoxy could do with sorting this out. And I have some other grievances!