To my mind, none of these actually qualify as "divided civilisational spaces". This of course depends on what you mean by "split" in this context. An actual example of a "split/divided civilisational space" would be Catholic-Orthodox and later Catholic-Protestant-Orthodox: fundamental divisions within the civilisational space that is Christendom. Arguably, the division of roughly the same civilisational pace into the Capitalist-Communist dichotomy might also qualify-- although I think that one is actually much less fundamental. More of a surface-level thing, that has no real staying power.
-The division of the territories of Roman Christendom from 565 AD into those territories that became Muslim and those that remained Christian in 750
This describes part of a civilisation being conquered by another. The civilisation that is thus partially conquered in a very comprehensive manner isn't
split. It
shrinks. Syria, for instance, is simply no longer a part of Christendom. It is part of Islam.
-The collapse of the Soviet Union, with Ukraine eventually aligning with the West, in contrast to both Russia and Belarus, who have both remained parts of the Russian world
The Russian sphere as it exists now is just the remnant of the historical aberration that was the USSR. The rest of the traditional "Eastern Orthodox" sphere has already been (re-)absorbed into what is (presently) called by the secular moniker "the West". The Catholic-Orthodox split has mostly ceased to be politically relevant in most cases (as has the Catholic-Protestant one). Russia is committing national suicide as we speak, so that's actually over, too. When the end is finalised, Western Russia will be re-absorbed into "the West", and the more Eastern regions of Russia (historically the "mongoloid" parts) will be grabbed or at least thoroughly vassalised by China, per its long-standing ambitions.
So what division? We are actually in the process of a somewhat messy re-union of Christendom. And the USSR was only ever a minor stumbling block in that regard. The more relevant historical trend is that Protestant, Catholic and Orthodox nations are already re-grouping under one umbrella.
-The division of Europe by the Iron Curtain during the Cold War
Barely relevant, as I mentioned. A temporary political division, with far fewer consequences than, say, the Hunderd Years' War. (And that didn't in any fundamental way split Christendom, either.)
-The split of Korea during the Cold War and beyond
I'm not convinced Korea constitutes a civilisational space. It's historically an appendage of the Sinic civilisation, really. Sure, it's independent now, but that's like saying Britain has split from Western civilisation because of Brexit. Obviously a non-starter.
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A real example of an ATL "divided civilisational space" would be if large portions of Germanic Europe suck with Arianism. Or if the Chalcedonian view had been prevented, and Christianity had become divided between the radical Antiochene and Alexandrine views. Or if either the Monophysites or Miaphysites had maintained power based in Alexandria against the Chalcedonians, thus creating a separate North African Christianity. Or if the Nestorians had prevailed in the East, thus creating a much larger (but also more internally divided) Christendom.
For comparison: I personally feel that if some form of Gnosticism had prevailed in parts of OTL Christendom, this would effectively see those regions break away and become a truly separate civilisation-- so to my mind, that wouldn't qualify, either.
But on the other hand, the Sunni-Shi'a split certainly qualifies.
We may note that religious divisions tend to be fundamental enough to create a long-enduring division (unlike most purely materialistic disagreements, which tend to be fairly fleeting), but that the remaining religious
commonalities also prevent the "divided" civilisation from completely breaking in two. So religion seems to be the main factor producing "divided civilisations", I would say.
