I‘m German, and you either don’t understand it yet or will never really get it.
The „he’s Turk“-comment was probably referring to culture and not nationality.
No one, except maybe AfD-voters and some AKK-supporters, would consider this person a Turkish citizen and rather use the word „Turk“ in order to describe cultural differences.
For example, I was friends with an afghani girl and I would visit her home, but her family, while really open, were all strict muslims. I felt welcome there, but their culture was very different from the „average (non-muslim)“-German. For reference, she was a second generation German.
Would you rather have it that Germans refer to people with different backgrounds as their skin tone or the culture they use to live their life?