I hope that my post isn't going to come off as demeaning, and I don't doubt your own experiences that people have hated your heritage. But the US does indeed have a dominant cultural standard, which can even permeate in isolated places.
In US society, most Western and Eastern Europeans are treated as white, as are several Southern Europeans such as Italians. Many hispanic people are technically multi-racial, but due to a misunderstanding of Latino identity society groups all of them into one race. There are many Latinos who self-identify as white, and many who have light skin might be viewed as white by the rest of America even if they themselves don't accept the label. Regarding Southern Europeans, their tanned features initially had them grouped outside of being whiteness, but US society accepted them into the white paradigm decades ago.Edit:
As for "white America," British laws, culture, language, etc permeated what is now the United States for decades, and even in the days of segregation culture didn't exist in a vacuum. African-American slaves adopted Christianity from Europeans, immigrants assimilated while retaining elements of their own culture, laws, school textbooks, etc pass down a universal standard. Even Native American reservations are affected due to the legacy of boarding schools banning many cultural elements in favor of the US/Anglo/pseudo-British ideals.
White Western European culture elements are a dominant force in the US. This isn't inherently bad in and of itself except when said culture is forced on others, and for the past few centuries voluntary and involuntary adaptions spread it everywhere.
Going back to Dhi's earlier posts, foreign people in American society are encouraged to assimilate. In some cases this is practical, like understanding the laws of the land for better community cohesiveness, but many times not wanting to pick up on the dominant culture will mark you as an oddity at best, or picked on and bullied at worst.
Apologies if I come off as speaking for you, Dhi, or anyone else.
White privilege is having white and Caucasian treated like dirty words. People assume that what you have was given to you and that you didn't have to work hard to get it.
This can cut both ways. Minority groups who have been historically disadvantaged in academia who end up getting a college scholarship or jobs can cause people to think that they didn't earn it by merit, but instead by affirmative action quotas.