Ignore the political aspects for now and focus on culture. And feel free to use "Roman" if "European" sounds wrong. But "Western" is wrong, because the same cultural sphere extends to Australia, New Zealand, and Russian Far East.
From my perspective, as someone from the Northern fringes of Europe, Latin American society and culture feel fundamentally familiar, while Middle East and North Africa don't. Out of the Latin American countries I'm most familiar with, Peru feels more European and Chile more American. Peru feels more like an Old World country, while Chile used to be a sparsely populated frontier.
Europeans definitely don't view other Europeans as kin. They are foreigners with a lot of shared history and culture. Both World Wars were fought because Europeans saw other Europeans as fundamentally different.
> But "Western" is wrong, because the same cultural sphere extends to Australia, New Zealand, and Russian Far East
Yes. And Australia, New Zealand, Japan, Taiwan, and South Korea are viewed as "Western" in American discourse as well. The Russian Far East isn't though.
> From my perspective, as someone from the Northern fringes of Europe, Latin American society and culture feel fundamentally familiar
> Out of the Latin American countries I'm most familiar with, Peru feels more European...
Frankly, a Finn isn't the right person to make this distinction. And if you've been to Peru you most likely spent the bulk of your time in Miraflores and other European parts of Lima, and not the majority indigenous hinterland. The European-Indigenous fault line is a major faultline in Peru going back to the Shining Path days.
I've spent more time in the Andes than in Lima. The Quechua are clearly an indigenous group, but they have been forced to adopt most of the European cultural package. If you travel in Russia, you can find many ethnic groups in similar situations.