Rome was Christian when the Western and Eastern empires were founded, and when they fell. My understanding is that modern West/East etymology is heavily influenced by the Western/Eastern Roman empires.

Yes, strictly speaking the West, the Occident, is born out of the leftovers of the Western Roman Empire.

>Unfortunately “western” is now seen as the Abrahamic judeo-Christian capitalistic worldview, even though the west sprang out of pagan Greece and Rome.

The west "sprang out of pagan Greece and Rome" when they decided to become Christian. The actual pagans had been slowly abandoning paganism as a dead-end and turning more into esoteric religions and neo-planonism etc and the influence of Egyptian etc religions for several centuries before Christianism was a thing...

>Native Americans and pre-Christian pagan Europeans had a lot in common.

Other than not having the Christian religion, no, not really.

>Both cultures that honor seasonal cycles, animals, nature, ancestors, animism etc

"Both cultures" ? What cultures ? Neither pre-Colombian Americas nor Europe shared a culture on their respective side. Even if most of Europe shared a common Indo-European root, religious practices were varying widely. Be it from the cross-pollination with different tradition (pre-Indo-European, Semitic and whatnot) or social changes. It's very hard to argue the official Roman religion as practiced in cities was any more "closer to nature" than Catholicism is.

>the Abrahamic judeo-Christian capitalistic worldview

Any more grand words to force into that sentence ?

Making the Christian religion itself being the deciding factor in your reading of history is a position that's very... Christian.