Purgatory is usually presented as Catholic doctrine denied by everyone else. That is accurate about the Reformation churches and misleading about the Orthodox, and the difference between the two rejections is worth having.
The Orthodox pray for the dead
They do it constantly. The dead are commemorated in the liturgy, on appointed Saturdays, at memorial services on the third, ninth and fortieth days. The Orthodox hold that the departed are genuinely helped by these prayers.
So whatever is being rejected, it is not the proposition that the dead can be assisted, and it is not the practice that the doctrine of purgatory grew up around.
What is rejected is the apparatus
The Latin construction placed around the practice: a defined state whose purpose is the satisfaction of temporal punishment still owed after guilt has been forgiven, with an accounting of that punishment which makes indulgences intelligible.
Mark of Ephesus argued exactly this at Florence in 1439. His case was not that the dead cannot be helped, he affirmed they can, but that the Latins had erected a doctrine, with a mechanism and a currency, where the Greek tradition had a practice and a deliberate silence about its workings.
The Protestant rejection is a different one
It denies that any satisfaction remains to be made at all, on the ground that Christ's satisfaction was complete. That removes the state and the practice together. The English Articles reject the doctrine as grounded on no warrant of scripture, and the clearest supporting text is in books the Reformers did not accept as canonical.
Two rejections, different in kind: one denies a theory built over a practice, the other denies the premise the practice rests on.
What Trent actually restrained
Having defined the doctrine in 1563, the council immediately limited it. Bishops were instructed to exclude from popular preaching the difficult and subtle questions, and to forbid the circulation of things uncertain.
That is a caution against precisely the material a reader will picture, the fires, the durations, the arithmetic of remitted years. Much of the popular image of purgatory is devotional literature that the council defining the doctrine tried to suppress.