I have come late to this topic not have I thoroughly read each and every post, so I apologize in advance for repeating thing said above.
First, I think a group should normally be allowed to regard themselves in a way they wish, and within reason we should acknowledge that. So we have used terms like Negro (Nigra, and worse), Colored, Black, Afro-American and African American. But even amongst the those self identifying groups there is no consensus.
If I were the determiner of which word to use, I would prefer Black, even though they are mostly not black, but a shade of brown. Brown, however, seems now to connote Latin Americans of some Indian descent.
Afro- or African American would seem to exclude emigrees from northern
Africa like Egypt, Libya Morocco etc., and long time Europeans of South Africa, Zimbabwe etc. to the United States. Also, what about black Africans who live here, but are not American citizens?
BTW, what hyphenate is used in Great Britain or France, if any? If none, I think them way ahead of us.
Back in the 60s, the term of currency for Caucasians was WASP. I used to object to being so labeled because I had no Anglo-Saxon, nor Protestant forebears, and that is still the case. Now I look on that term as a stupid appelation and just laugh about it.