What do you mean by "roots"? It looks like we are thinking of different meanings. I think you are strictly thinking of "origins". I use "roots" as something that can be developed over time, as in "take root" and I take seriously the development of these roots over centuries. Contrary to ancient Athenian belief, people don't spring up from the ground (autochtony), they wander and take root. Ultimately we all originate from some African plateau.
Greeks did not originate in Asia Minor, but by the time Alexander set off to conquer Persia, they were extremely well rooted in the coastal regions and were already a core part of Greek civilization.
The Huns disappeared. The Magyars on the other hand didn't. Yes they originate in the steppe, but they are deeply rooted in Hungary.
As to whether Christianity dissects Greek culture, and as to how profoundly that is, ...well, άσε και σε μας τους Έλληνες να έχουμε μια άποψη για τον πολιτισμό μας.