Thanks for sharing your story.
The focus of the campaign is the narrow topic of 'white privilege'. Do all white people in America occupy the exact same strata in society? No. Immigration and language/cultural barriers are unique obstacles. I don't think the campaign for what it is or trying to do can expand to include a more comprehensive breakdown of society. It is simply trying to make the biggest mark in the biggest absence (of people of color literally and race consciousness generally) in "the whitest city in America".
As for the larger question about white privilege? The fact that white privilege exists does not mean "all white people are rich" or "able bodied" or "have easy lives". It is a relative privilege, meaning that "all other things being equal" you will have a leg up due to phenotypical "whiteness" compared to someone in a similar situation as yourself. And yes, being an immigrant, even a "white one" is an extension of 'otherness' which plays on similar preferences and systems that 'white privilege' does. Even with being an immigrant the experience is vastly different for people depending on the circumstances of their migration, poverty, education, language, etc.
I think in the context of immigration, as I'm an immigrant also, you see the privilege work especially generationally. 2 generations from now when language and cultural barriers and hardscrabble origins are a distant memory, your grandkids (unless they are visibly/phenotypically multi-ethnic) will be likely be seen as 'all-American' and get full benefit of white privilege whereas my grandkids (unless they are visibly/phenotypically not read as 'multi-ethnic') will not.
Hmmmm...I think I'm losing my train of thought....
Who else might be able to contribute.. @Eileen?