From what I know, they’re a schism. Why then are they not considered Protestant?
I am aware the schism occurred a long time before the Reformation.
The context of the division between Catholic and Orthodox Christianity - historically, theologically, culturally, and otherwise - is entirely and qualitatively distinct from the context of the division between the Catholic Church and the Protestant movements.
What makes a denomination “Protestant” isn’t just the fact that it’s a group of non-Catholic Christians. Here in North America, Protestants are so common that it may sometimes seem like “Protestant” just means “non-Catholic Christian,” and therefore that Orthodox may as well be Protestants, too, but
that’s nonetheless a mistaken impression: it’s actually
not true that all these denominations are Protestant because they’re non-Catholic.
Rather, the reason they’re Protestant is because, in some way or another, they are descended - theologically and historically - from the radical reform movements of western Christianity’s sixteenth century history.
Every single one of them. Even the “non-denominational” types are basically *de facto *Baptists. Even seemingly neutral denominations - like the “Church of Christ” - are offshoots of other Protestant denominations. Methodists came from the Church of England. Episcopalians did, too. Presbyterians come from Calvinists. The Baptist, non-denominational types come from Anabaptists. And the list goes on.
So while Protestantism may seem like a group comprised of individuals with basically nothing in common other than being non-Catholic Christians, their history and theology are all ultimately rooted in the sixteenth century movements and leaders we identify as Protestant.
That and
that alone makes them Protestant.
So the short answer to your question is
that Orthodox Christians aren’t Protestants because their church and their faith have nothing to do - theologically or historically - with those western, sixteenth century radical reform movements.
Their identity and their faith predate Protestant Christianity, and they have remained largely unaffected by Protestantism. Their seventeenth-century Synod of Jerusalem rejected some beliefs that were under discussion due to the existence of Protestantism, but that’s about it.
So that’s why they’re not Protestant. Does that make sense?
In fact from the Orthodox point of view they considered Rome to be Protestant.
I think both the OP and your response underscore why it makes sense that the norm is to identify three different varieties of Christianity in the broadest sense: Catholic, Protestant, and Orthodox.
Because it’s nothing new for members of one variety to basically say, “Yeah, you other two are basically exactly alike.”
I know some Protestants who can’t tell the difference between Catholic and Orthodox Christianity (from their perspective), and as you’ve pointed out, some Orthodox basically consider Catholics and Protestants to be one group, for all intents and purposes.
And then, of course, there are the Catholics who think of Catholic and Orthodox Christianity as basically united already.
All of these are, of course, oversimplifications. That is why to speak of
three varieties of Christianity remains the commonly accepted framework.
I see, though they don’t follow the pope, which I would think is a pretty vital aspect of Catholicism
It is a vital aspect of Catholicism. That’s why Orthodox are
not Catholics.
That’s what I’m trying to say here, to everyone:

Catholic, Orthodox, and Protestant Christianity comprise three distinct forms of the faith. To conflate two of them - whether Orthodoxy and Protestantism, Catholicism and Orthodoxy, or Catholicism and Protestantism - is seriously problematic.
What about Anglicanism? I’ve always considered Anglicans more similar to Catholics than to Reformed Protestants (though that’s just opinion).
Their identity, both aesthetically and theologically, has shifted a great deal throughout history. In the Edwardian and even Elizabethan/Jacobean era, they were
very Reformed. In the Caroline age, they became really “Catholic” again, but they’ve always varied.
Today, some Anglicans consider themselves Protestant, some consider themselves Catholic (the Catholic Church disagrees, of course), and some consider themselves a fourth branch (which I find unrealistic, as their roots do lie in the Protestant movements of the sixteenth century).
In some ways - liturgy, most of doctrine - they’re very Catholic. In other ways - moral theology, etc. - they’re very Protestant. So it’s a mixed bag.
I consider them Protestant, because, well, that’s really the most historically reasonable position. They didn’t just pop into existence; their roots
are in Protestant Christianity.
Protestants believe in justification by faith alone and the Bible as the primary authority for the Christian and the Church. Protestant churches also have a different understanding of Apostolic Succession. Some deny it completely. Others (like Anglicans and Lutherans) still have it but don’t place as much importance on it as Catholics do.
The Orthodox don’t believe in any of that. Therefore, they are not Protestants.
Well said.