I wouldn't say I shun it (I'm very pro-white in the face of too much political correctness, or in the face of reverse racism, also known as "affirmative action"), but I don't stay in lockstep with it either, and I'm quick to criticize it.
--90% of my friends are some kind of ethnic minority
--Everyone I dated (and who I married) was non-white
--I enjoy ethnic cuisine far more than most white people, even by the L.A. standard.
--My musical tastes straddle multiple cultures and outlooks, and I'm not into Metal, Alternative, or any other stereotypically "white" musical genres.
My main issues with white culture have to do with some of the cultural snobbishness. I'm just as guilty of this, but I don't like being too insular. By the same token, I also don't like it when other ethnic groups are too insular -- this is America, we're supposed to blend, not be "separate but equal."
However, I also don't like it when white people (or any people) are too politically correct or too into the "white people are to blame for everything" mode that became so popular in the 1980s and beyond. I especially don't like the idolization of thug culture and ghetto black culture that started mainly in the 1990s here, though this has also happened in previous eras in this country (the 20s and the 60s). Putting an ethnic group on a pedestal that has had every chance to make things right with themselves, has had the country tripping over itself to please them for the past 50 years, yet still commits a disproportionate amount of crime, wallows in poverty and births out of wedlock (70% now, vs. 20% pre-Civil Rights), and if anything, has made the mainstream culture worse and trashier with their ghetto culture doesn't seem like a great thing to me. I don't think white guilt is a good reason to pander and turn a blind eye to self-inflicted problems in that community. Everyone else seems to be able to get with the program, why not this group?
Anyways, that rant aside, I don't particularly identify too much with other white people other than some common roots. Having married someone of another race and nationality has opened my eyes to the difficulties others face, and some of the wrong cultural assumptions we make.
P.S. -- I know Seattle has more African Americans than it used to, partly because of CA's third strike law, and partly because poorer immigrants pushed them out of neighborhoods here in L.A. (Compton is now a majority Latino), but have you actually been to Atlanta or the South at all? I can assure you that the African American folks you find out there will be a far cry from what you experience in Seattle, and not in a good way. I for one have been fairly shocked by the level of poverty and crime that the South has, even compared to the gang warfare and daily homicides we have out here in L.A. It really is the pits out there.