It is indeed notable that Bigger receives better treatment from rich whites than poor ones. For the most part, this is to do with differences in education. Educated whites such as the Daltons tend to have more enlightened views on race, believing as they do that race is an artificial social construct. In addition, rich whites—though the vast majority of them are Republican—tend to supply many of the leaders of radical political organizations such as the Communist Party, who advocate the formation of a brotherhood of the oppressed as a means of overthrowing the capitalist system.
If one were being cynical, one could also argue that the Daltons's respectful treatment of Bigger is due to the fact that they don't feel threatened by him—at least not in the economic sense. Unlike poor whites, who find themselves in competition with African-Americans for low-paid jobs, the likes of the Daltons are protected from this daily struggle for existence. As such, they have the luxury of being able to develop a more progressive consciousness when it comes to the issue of race.