While flipping through the book though I found this great paragraph from Chapter 16: The Reality of White Privilege that I'd like to share:
We are trying to get a sense of white racial privileges - distinct from the surplus taken by the white ruling class through exploitation. To do so, we want to focus as much as possible on differences within the broad working class. As described in earlier chapters, the white owning class in the United States exploits both white workers and workers of color. At the same time, the system affords white workers certain racial privileges that they have often jealously defended despite their exploitation. The white ruling class exploits both white workers and workers of color - and uses racial privileges to sustain their rule. White workers benefit - in comparison to workers of color - while at the same time being exploited for their labor power. This distinction is crucial. It points to the fact that ending exploitation - and the system of racial privileges that support it - is in the interests of white working class people as well as people of color. (italics are Smith's, bold mine)
In order to truly take up true class consciousness, in order to shed the oppressive bourgeois mindset that paralyzes many workers (especially many workers at my job who would rather support management than the union), a white worker must shed her or his whiteness and all privileges that come with it (or, perhaps, a more appropriate term would be reject).
Which reminds me. If any of you can find it out there, the book (out of print) Settlers: The Myth of the White Proletariat by J. Sakai would be a good complementary read along with The Cost of Privilege. (Some Marxists and anti-racists take issue with Sakai's analysis, some even call Sakai slightly mad, but hey, good read and informative).