I did just suggest they change it to “The Doc” but I don’t think they’ll go for it. 
I suspect their motivation might be for the rhyme? But aside from the dubious racist overtones, unless people are very familiar with him and his show, would they know he’s ethnically Turkish? I mean, I guess when I think about I knew his first name, so if you asked me to guess his ethnicity I’d probably get there. But if you just said “name a famous Turkish American” I’d have been struggling to think of Oz.
“The Quack” would be wholly accurate and also not sound racist.
They’re trying to rhyme it with jerk, aren’t they?
My mother’s husband (technically, my stepfather) was Turk. Only he was born in Finland. 
Yup, this is much better. If you said “name a prominent quack”, he’d be the first name that came to mind.
And easy to find rhymes.
In the Leeward Islands are Turks and Caicos, the former named after cactuses that look like they’re wearing funny Morocco Mole hats. That’s downright insensitive and needs changing
…right after we go over to the Windwards and speak with the Grenadians about that Jew Bay.
What do the people of that country prefer to be called? That’s what we should use.
When his race is irrelevant, the question is why it’s being mentioned at all. It depends on exactly what is said and the context, but it may be taken to imply some kind of racist generalization about people of that race.
Especially given that he’s American, rather than a Turk - or even (presumably) Turk-ish.
Insulting to Anatidae.
Agree. If the point of the reference is to subtly remind the audience that he’s an untrustworthy furriner from a distant country with mysterious ways and should be discouraged from office on those grounds, then that’s over the line. National origin is (with very, very narrow and limited exceptions) irrelevant as far as qualification for elected office and public service.
Unless it’s supposed to be tongue in cheek and there is also an equivalent swipe at his opponent, calling him The Redneck or something. Then it might be defensible. But this still feels like a bit of a reach.
The Dr Oz who was born in Cleveland? Surely he’s Turkish-American, not a Turk.
Agree. I think a lot of the time people would like it to be absolutely defined that word X is a slur and Word Y is not, but it just doesn’t work like that - context, intent and effect of phrasing are important, because prejudice doesn’t happen on the page, it happens in behaviours and thoughts and intentions.
Is his opponent similarly being called ‘The Scotsman’ [Irishman, Spaniard etc] in reference to the origin of their family?
If not, then its Oz’s ethnicity being used to delegitimise him as not being as authentically American as his opponent.
Its racist and dog-whistling.
I believe he spent a significant part of his childhood resident in Turkiye.
Is that relevant to the rest of the sentence? Or to the rest of the song?
I’m a Jew. I’m happy to be called a Jew when that’s relevant. But if you wrote a satirical song about my political candidacy, and referred to me as “the Jew”, yeah, I’d think you were anti-Semitic. And I’d probably be right.
I don’t think that matters, for his nationality.
He has Turkish citizenship and he apparently did the National Service.
ETA: I don’t doubt the [person quoted in the OP had less than honorable intentions.
Neither do I.