I think it can be, it depends on the context.
I have two black friends both of whom I've known for years. One, originally from Jamaica, born there, but came to England as a baby, she will talk about her heritage and origins quite often, particularly in the context of DNA, she has often pointed out to me that her given surname came from whoever owned her ancestors and she can only get back so far with her family history which she is very into, we both are, I've had my DNA analysed and my ancestors also came from a number of places in Europe. . For her though it is entirely different having antecedents born into slavery but now thanks to DNA she at least knows which part of Africa her origins lie. My other friend, came as a baby from Sierra Leone, her parents came to England as students ,left her with a white foster family when they went back to Sierra Leone, then came back for her when she was around eleven years old, she kicked up merry hell for one thing she didn't know them and allegedly refused to go back with them. The upshot of that was they left her with her white foster parents who were later to adopt her. Probably wouldn't be allowed now but she is well into her 60s and things were different when she was growing up. We learnt all this from her late husband who was one of my husband's close friends. It's a subject she never brings up, I don't think she wants to talk about it, so we wouldn't either, she refers to Essex as where she's from and I think she'd be very affronted if she was intrusively cross questioned in the Susan Hussy manner, who seemed devoid of any tact or emotional intelligence. It's not that difficult to gauge if people are reticent to talk about what may be a sensitive subject.