That would be the Maniots of Laconia. Laconia is a region located in the southernmost tip of Greece; it is composed largely of swamps and mountains, which makes it very difficult to establish the same sort of large cities and communication routes that developed in the rest of the country. The Maniots were a group of people who had, by the time of Roman Greece, inhabited these lands so far back that they were mentioned in the Iliad. They too practiced the ancient Hellenic polytheistic religion that the rest of Greek culture did, with a few minor variations.

Enter the 5th century AD. By this time, the Roman Empire (well, more specifically the Eastern Roman Empire at this point) was rapidly experiencing a Christian dominance in all levels of social and political life. Emperors during this time period released edict after edict imposing stiffer and stiffer penalties upon pagans, up to and including death. The last known formal pagan resistance to Christianization came in the form of General Leontius, a military commander who rebelled against Emperor Zeno in 484. Part of his appeal seems to have been a promise to restore pagan values and culture to the empire. He ended up losing the revolt, which led to a final clampdown on paganism empire-wide from which it never recovered.

However, the Maniots of Laconia seem to have been insulated from all this. The Mani Peninsula, as I noted above the mountainous terrain and difficulty of enforcing laws in such a region probably was a contributory factor. The last association between the Maniots and paganism seems to be in 804, when Saint Tarasios attempted unsuccessfully to convert them by force. After that there is no mention of any openly practicing pagan group in Greece. Certainly they were Christianized sometime in that century, because Emperor Constantine VII (who reigned 913 - 959) wrote the following about them:

Be it known that the inhabitants of Castle Maina are not from the race of aforesaid Slavs (Melingoi and Ezeritai dwelling on the Taygetus) but from the older Romaioi, who up to the present time are termed Hellenes by the local inhabitants on account of their being in olden times idolaters and worshippers of idols like the ancient Greeks, and who were baptized and became Christians in the reign of the glorious Basil. The place in which they live is waterless and inaccessible, but has olives from which they gain some consolation.

This also addresses your second question of whether they were considered hillbillies. The answer seems to be yes. This excerpt is a fairly dismissive and uncharitable description of the Maniots, only begrudingly acknowledging that their existence has "some consolation" in the form of tasty olives.

Source:

Greenhalgh, P. A. L.; Eliopoulos, Edward (1985). Deep into Mani: Journey to the Southern Tip of Greece.