As a middle-class white kid growing up in Washington, D.C. in the 1980s, The Cosby Show was a tremendously important show that was not only totally "appointment TV" but also helped me develop my growing sense of fairness, love of family, and racial visibility. Acham is totally correct in her article that the show was not about the blackness of a black family and only occasionally dealt with racial issues. At the same time, having a black family on TV every week (and quickly syndicated several times a day) was significant for me. Living in Washington, where the population at the time was about 65% African American, I didn't really understand that showing a black family was unusual. I took for granted that some families were white and some were black (both inside and outside my school). The Huxtables were probably more like my family, with two working parents—albeit with more kids than in my house—than many other families on television (Silver Spoons, Who's the Boss?, Kate & Allie). I knew they did not physically look like me, but it felt similar to my experience (probably aided by my dad, like Cliff, also having his office in our home).
Acham points out that the cultural specificity of the Huxtables was a half-step removed from the thematic content of the episodes, for instance, the art on the walls including "[paintings] by African American artist Varnette Honeywood...hung in the [the] home. There were also framed pictures of African American historical figures such as Martin Luther King and Frederick Douglass" (107). She doesn't mention how the costumes on the shows were frequently more related to black fashion than white trends. Cliff became a fashion plate for amazing sweaters, which were not necessarily black, but also not conservative the way a white Ob/Gyn would otherwise dress on a network show. (Just googling "Cliff Huxtable" now, the first autofill suggestion is "Cliff Huxtable sweaters".) The eponymous item in the iconic episode "A Shirt Story," where Denise makes Theo a copy of a designer shirt to save him money, would have been unlikely to appear in the closets of many white teens. There was never a question for me that I was watching a show about an African American family, however I think not confronting many issues related to race made their difference from me something that became a asset rather than a deficit.
Following this show (and A Different World, which was better than The Cosby Show in its later seasons, though took a similar reticence about dealing with many overt issues of race, even at an HBCU), The Fresh Prince of Bel-Air was probably the next family comedy I watched that focused on a black family. The added complication here was that it showed that some families (black, white, or otherwise) have more complicated structures. I didn't know anyone who lived with people other than their parents and it was important for me to understand that family structures did not have to be "traditional" (in a Moynihan Report sense). Following this, I loved The Bernie Mac show (produced by Larry Wilmore), which added another complication to the Cliff Huxtable/Philip Banks father-knows-best model. The show's premise is that Mac, playing a fictionalized version of himself, is raising his sister's three kids because she is struggling with drug addiction. (If you haven't watched the show you should because it's hilarious.) The show knows it's on the same family road as Cosby, but it takes a different angle by dealing with issues of race directly. I don't know if it would have been as successful if the audience, black or otherwise, had not "grown up" with the model set by Cosby.
Today we have Black-ish (also produced by Wilmore) and I wonder if this is the postmodern response to all of these shows. It's about blackness, but also about being a family. It shows the complicated nature of parents and kids regardless of where they live or the color of their skin. It knows who came before it and sometimes pokes fun at its influences and itself. Meanwhile, even when it doesn't directly deal with issues of race I think a non-black kid growing up today and watching that show will appreciate that it's about a black family, full stop. The visibility of difference means a lot to all viewers.