As I've also mentioned, Greek is not the only language spoken by the ethnic group around Mariupol. A minority instead speak the Turkic language Urum.
A group identifying itself as Greek and Christian but speaking a Turkic language is a challenge to the levelling impulse of modern nationalism—and far from the only one. At the Other Place, I posted what was going to be the lead-in to this post: its maudlin meditations on identity were more appropriate there, and I ended up talking more about the Karamanlides than the Urum anyway. But there's still some sociolinguistic outcomes of the situation that it's worth going through here.
Urum is a variant of Crimean Tatar, a language distinct from Tatar and closer to Turkish. The language came with the Greeks from Crimea. The entire ethnic group moved to Mariupol in 1778, invited by Catherine the Great to bolster the local Christian element: the fact that some of the Christians spoke the Muslims' language obviously wasn't a concern before modern notions of nationalism.
Crimean Tatar was the "bazaar language" of the Crimea, its language of trade and of dealings between speakers of different languages. One of the main reasons Mariupolitan Greek is so hard to understand for Standard Greek speakers is its profusion of Tatar words. And even though Urum is closer to Turkish than Tatarstan Tatar, it's still different enough for those loans to sound somewhat off-kilter to Standard Greek speakers, compared to their own loans from Turkish.
How it came to pass that a group of Christians spoke Tatar and followed Greek-speakers to the Ukraine is a question we're not equipped to answer. The lazy answer is that they were Greek-speakers who switched their language, presumably in villages with a majority Tatar population. There were penalties against switching from Islam, so it is an easier answer than the alternative, that they are Tatar-speakers who switched their religion. Still, it would be foolish to get too precious about notions of Hellenic DNA—especially when we can be reasonably sure there is Gothic blood in the Mariupolitans, with the last (and first) documented speakers of Crimean Gothic switching to Greek, and their bishop in Crimea still being the bishop of Gothia. (It would be foolish to get precious about DNA in general, but that's a topic for the Other Place.)
The Urums felt Greek enough to move to the Sea of Azov, and they feel Greek enough to call themselves members of the Greek ethnic group (and to call their Turkic Greek: their "Urum" corresponds to the Mariupolitan Greek's "Rumeyka"). But there was some sense of separateness, because the Urums and Grecophones did not live in the same villages in the Ukraine (18 Grecophone, 15 Urum villages), and E. Perekhval'skaya (whose online description I am using extensively, via Google Translate) thinks that sense was already there in the Crimea.
The Urums' language was still, to some perspectives, the "wrong language" for Greeks to be speaking. This was not particularly an issue under Ottoman or Russian Imperial rule, when language wasn't much of an identity determiner anyway. But as I posted in the Other Place, once Turkic speakers find themselves in a Greek nationalist context, they will be pressured to drop Turkic—and the Karamanlides would likely have been all too happy to comply.