First of all, I reject the phrasing of your question. The US continued to exist as a "truly" racist society after Jim Crow. Certainly, the end of Jim Crow was a blow to the legal basis of structural racism but it would not topple the edifice altogether - as is shown in all historical scholarship dealing with race in the 1970s and 1980s. And, looking at your other posts, I'm sure that this phrasing is purposeful on your part.

But, if we are to proceed on the assumption that you aren't being disingenuous, then it depends upon which period in Jim Crow you mean. Certainly, it would have been seen as a bizarre question during the 1920s; while there had been some discussion surrounding "race prejudice" and "negrophobia" during the late 19th century, these terms were not common in popular parlance, however, and were largely related to discussions surrounding public policy. Although, I should add, if you phrased the question slightly differently there would have been a great deal of spirited rejection of the idea that black peoples were the philosophical and moral "equals" to "whites." By the end of the Second World War, the idea might have gotten more traction - as by the end of the 1930s there was some idea that fascist policy in Nazi Germany were "racist" in the sense that they highlighted and presumed a racial hierarchy that structured their world. In the US, perhaps somebody might think that you were asking if they subscribed to those ideas - and during the mid-1930s you might even find some "yes's." As the war ended though, as others mentioned, the notion would have been linked to the Nazi crimes during the Holocaust and fallen to disrepute.

During the Civil Rights period, citizens would likely have known what you meant but framed it as a policy question about the Movement itself or the end of Jim Crow. Similar to what the above commenter wrote, there would have been a sense that black Americans were "more suited" to menial jobs and positions and perhaps didn't have the capacity - nor, for the most part, the desire - to fully participate in modern society. On the other hand, there also would have been the acknowledgement that much of the treatment suffered by black Americans was "unfair." And of course, these notions would change depending on who, specifically, you were having these conversations with and where the occurred.

See, as source material, David Brion Davis's 2014 book The Problem of Slavery in the Age of Emancipation and his article on Constructing Race in the 1997 edition of the William and Mary Quarterly.