I think it may be a bit of both. A large part of the negative sentiment towards muggleborns seems to come from the purebloods viewing them as interlopers into a superior culture that has no place for them, for which the nouveau riche are the perfect analogy. But at the same time, the conflict has a great deal to do with ancestry and heredity; Voldemort and his coterie, evil bigots that they are, want to stop the muggleborn outsiders from diluting their superior bloodlines, a clear echo of various racist ideologies. The tie is made even more explicit by Rowling's depiction of Grindelwald, Voldemort's predecessor as a Dark Lord and pureblood supremacist, who has a biography that carefully echoes Adolf Hitler's. Rowling is sometimes unsubtle.

(Disclaimer: I've read an embarrassing amount of fanfiction, and have sometimes been known to confuse canon and fanon.)