Greece was an Eastern country in 1832, and has been telling itself ever since that it’s a Western country. (That’s what the Westerners were telling her too. At least, to her face.)
By the 1990s, Greece was a Western country. But the Eastern roots are still there.
When the switchover between East and West happened is hard to answer. I think it’s the 1980s, others might think it was the 1880’s.
There’s been a lot of talk here on Quora about Greeks calling themselves Roman (Ρωμιός). The Hellene/Roman dichotomy is the Western/Eastern dichotomy.