I spent a few years in Michigan, and was all but told this. In one conversation that stuck with me, a chap was on one of his frequent rants about "them", and I felt compelled that he was ranting about immigrants, to an immigrant. His responses included "you know what I mean", and "at least you bothered to learn the language".

As an Englishman, "at least you bothered to learn the language" tickled me pink; but "you know what I mean" really stood out to me. Yes, we do know exactly what they mean, but they'll entirely deny meaning it.

I realise the plural of anecdote isn't data, but there's certainly at least "some" people who feel that white immigrants are acceptable immigrants. This was during the late-bush/early-obama period, so I'm poorly placed to judge whether the scale of this has changed.