From my experience, black people want to be called black. I’m a white kid, but was raised in a foster family with three black siblings and other black family, including some that lived in a ghetto in another city. It was the 90s and early 2000s, so we watched some BET, we watched the Boondocks, we listened to thug rap, we watched shows with black characters such as All That and Cousin Skeeter. Because it was all a part of my brothers’ culture, and they felt attached to it, and “black culture” was cool to all of us. And in anything we participated in I’ve never heard a single African-American who didn’t call themselves “black” and be fine being called that. Maybe there are some rich people like Obama or Tom of The Boondocks who wouldn’t call themselves “black”, but they seem to be of a different lifestyle and culture than that.
I’ve also sometimes made the argument in defense of “black”, that “African-American” is mildly politically-incorrect itself— not that I have a problem with the term, just the hyper-vigilant enforcing of it. Because it’s not synonymous with skin color itself, it’s a statement about where they came from. We don’t call white people “European-Americans”; and what do we call non-black African-Americans from, say, Egypt or South America? So… yeah.