First, we must realize that it is difficult to answer this question with any certainty. There were no scientific opinion polls in the 1920s. Therefore, we have no statistical data to tell us what percent of the people felt that segregation was acceptable. We can only infer their attitudes from other evidence.
The other evidence strongly implies that Americans on the whole did not care about segregation. They did not see it as any sort of an injustice. African Americans surely did see it in this way, but they were a minority and lacked almost any political power. We can infer that whites did not care about segregation because there were no outcries against it or attempts to do away with it. There were no protests about the fact that African American soldiers in World War I had been discriminated against as they served their country. On the home front, there were instances of murders of African Americans who tried to live in white neighborhoods. In short, there is very little to give us any impression that white people were unhappy with segregation.