Christ is Born! Glorify Him!!
Hello Magic,
I would like to comment as an interested outside observer. You may (and should) feel free to disagree with these thoughts of mine, with which I only attempt to broaden the perspective, if possible…
…it implies a faith identical to that of Eastern Orthodoxy, which to be sure, is anti-Catholic…
I am not going to agree here.
It is fundamentally impossible for an Orthodox Christian of any sort to be anti-Catholic. I would say that it could possibly be termed anti-Ultramontane. Which (Ultramontane) to my thinking is a party of thought existing within the Catholic church.
I think possibly that the Melkites are in communion with Rome because they see it as a right and an obligation, not as a privilege.
I do not know why the Melkites remain Catholic while having an anti-Catholic faith, and it also seems to bear witness to the fact that the East and West are firmly divided even if communion between Churches has brought about union in this present day and age

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Again, it is fundamentally impossible. But there they are, which means your basic assumptions must be wrong. What you and some others might be bearing witness to is the unreadiness of the Roman Catholic church to accept Orthodox as equals. At least that much is revealed by these numerous posts about them.
I think the problem here is that UltraMontanism had hijacked the Roman Catholic church in recent times (although it’s influence…once strong… is definitely waning) and it has convinced many within the Catholic communion that it’s interpretation of what it means to be a Catholic is THE ONE interpretation.
I disagree (of course). I think that it is an encouraging sign that many Eastern Catholics (even prelates!) are feeling confident enough to express an independent (not original) line of thought, one very much in keeping with an earlier position of their churches. They are not really alone, RC bishops and even Cardinals have been known to express disagreement with some results of the Ultramontanist line of thinking. Even recent Popes seem to have been seeking a way around some of the UltraMontanist absolutes which have hamstrung their work, if I am interpreting their actions correctly.
Why do such individuals stubbornly remain in communion with Rome? I guess because they believe that it is important. You can (and many do) make all kinds of thrilling arguments about the importance of being in communion with the bishop of Rome, and people will listen intently.
But if you think that they will automatically follow a line of reasoning from that point to Universal Jurisdiction of the Bishop of Rome as defined in 1870 you have a much harder case to make. The one does not really follow the other automatically.
Quite clearly, the Melkite Orthodox church was not asked (in the 18th century, when everything came together) to submit to Universal Jurisdiction of the Bishop of Rome. They simply came into communion. UltraMontanism was not yet in full flower. The Papal doctrines, when expressed at all, were theologumena, held by some but not everyone.
The Melkite Orthodox of Antioch could not be forced into this decision, or coerced in any legal way. They did this thing because they very much wanted to. It split the synod, a huge sacrifice on their part…being divided from nearly half of their brothers and neighbors.
It was a great tragedy for those Orthodox Melkites who could not go with them, out of conviction.
Everyone lost something in the transaction. It is truly sad.
The deal they accepted was not the one Pius IX attempted to impose upon them later. They accepted an ideal where they still thought of themselves as Orthodox, still did not teach the filioque (nor teach against it, they ignored it not out of respect “for the west” but out of hope in Christs’ prayer that all may be one), and did not teach purgatory or indulgences. But they, unlike Orthodox elsewhere, were in communion with Rome.
Even they, relative newcomers to the Roman Communion, have still a longer history in communion before Vat I than afterward, with a continuous fully formed concept of their own ecclesiology which spans all of the centuries back before those days.
What happened in the Vatican Council 145 years later (from circa 1724AD or so) was nothing less than a “bait and switch” scheme from that perspective. Their Patriarchs seem to have exercised Patriarchal prerogatives to insulate their people from the worst effects of it as best they could, for as long as they could.
Make no mistake about it, like you I too must sometimes wonder why any of the Melkites are still in Communion with Rome. Especially after what has transpired in the Communion these last 14 decades.
But in them I see great possibilities.