Thank you for giving your opinion on what Eastern Catholics must believe, but as an Eastern Catholic I do not believe in purgatory, because that theological opinion is not a part of my Church’s (i.e., the Melkite Catholic Church’s) tradition. As far as prayers for the dead are concerned, Eastern Christians pray for the dead because we do not know their state of existence in the eschaton. Praying for mercy is a good Christian thing to do, and one can do that without accepting the Western notion of purgatory.
I didn’t just pull it out of my hat.
melkite.org/eparchy/bishop-john/how-do-the-popes-encyclicals-and-teachings-impact-on-the-melkites
Note the question being asked. Note the answer by the bishop. Did he deny purgatory was to be believed? No
In particular, I thought this was a great response.
“*Catholic is Catholic and truth is truth. We cannot pose as “Orthodox united to Rome” only for what suits us. I do mean it when we pray every day, at the Divine Liturgy, for “unity of faith and the communion of the Holy Spirit.” *
There is no ‘Eastern truth’ vs ‘Western truth’. Truth is one. It may be articulated according to various cultural expressions, but truth is super-cultural. Truth should not be restricted by “party line” positions. We should accept or reject ideas for their worth and not for an artificial attachment to a given “identity.” The Church teaches truth. If something is true, it would be absurd to say “Oh, we don’t believe that in the East.” This seems to be where we get short-circuited in ecumenical “dialogue.” All too frequently, such “dialogue” seems to presuppose a relativism where you speak “your truth” and I’ll speak “my truth” and we’ll just leave it at that. A sort of ecumenical schizophrenia.”
[snip]
"If we leave the Catholic position, can we still pretend to be Catholic? "
space wouldn’t allow me to further quote this bishop. So I gave the link instead

A:
St. John Chrysostom is talking about hell, as is clear from the text when read as a whole. After all, he says that the punishment is “forever,” and so I suppose there is no difference between the East and West as long as you believe that St. Augustine’s purgatory never ends and is really hell (gehenna).
Here’s what you posted again. (emphasis mine)
"If any man have an ill life with a right faith, his faith shall not shelter him from punishment, his work being burnt up. The phrase, “shall be burned up,” means, “shall not endure the violence of the fire.”
But just as if a man having golden armor on were to pass through a river of fire, he comes from crossing it all the brighter; but if he were to pass through it with hay, so far from profiting, he destroys himself besides; so also is the case in regard of men’s works. For he does not say this as if he were discoursing of material things being burnt up, but with a view of making their fear more intense, and of showing how naked of all defence he is who abides in wickedness. Wherefore he said, “He shall suffer loss”: lo, here is one punishment: “but he himself shall be saved, but so as by fire”; lo, again, here is a second. And his meaning is, He himself shall not perish in the same way as his works, passing into nought, but he shall abide in the fire.
[snip]
I guess I’m not reading this the same way you are. If one goes through this and comes out brighter on the other side, that suggests to me purification.
(quote cont)
"He calls it, however,
Salvation, you will say; why, that is the cause of his adding, “so as by fire”: since we also used to say, “It is preserved in the fire,” when we speak of those substances which do not immediately burn up and become ashes. For do not at sound of the word fire imagine that those who are burning pass into annihilation. And though he call such punishment
Salvation, be not astonished. For his custom is in things which have an ill sound to use fair expressions, and in good things the contrary. For example, the word
Captivity seems to be the name of an evil thing, but Paul has applied it in a good sense, when he says, “Bringing into captivity every thought to the obedience of Christ.” And again, to an evil thing he has applied a good word, saying, “Sin reigned,” here surely the term
reigning is rather of auspicious sound.
And so here in saying, “he shall be saved,” he has but darkly hinted at the intensity of the penalty: as if he had said, “
But himself shall remain forever in punishment.” (St. John Chrysostom,
Homily 9 on 1 Corinthians) "
If one goes to hell, it is an intensity that lasts forever, they are not saved in any sense of the word, there is no getting out. Chrysostom seems to be talking about 2 different cases. One soul is saved through the process, the other isn’t. Either way, one comes out shiney on the other side the other remains in the fire.