Perhaps eugenics was applied to both blacks and marginal whites (immigrants as well as 'white trash'), but it was applied differently in each case? I think that Rakesh's argument that blacks were racialized while Euro immigrants weren't still stands, with some modification.
Without the presence of racialized blacks, the fear of whites becoming 'like' blacks or even becoming black doesn't make sense. My reading of literature of the application of eugenics to the invention of the 'white trash' mythology makes me think that there was this constant fear that 'white blood' was becoming weak, enfeebled, diluted, exhibiting the features of 'blackness,' etc. So I think that racialization of blacks provided an overall framework for thinking about 'whites' on the margins of whiteness, both marked by ethnicity and class.
Fear of 'inbreeding' and that of 'miscegenation,' I believe, are both sides of the same racial coin.
Yoshie