Sascha Lilley recently did an interview with Amy Sonnie and James Tracey, and largely what I gathered was that the various white-oriented leftist movements especially among the working class were heavily involved with "racial" struggle. The Black Panthers, after all, were outspoken communists. Obviously there is a "continuing significance of race", but it would do us well to remember that Italians, Irish and Jews (and sometimes Scotch-Irish, save that they settled in remote enough areas to become dominant and normal) were initially held to be racially, i.e., bioculturally, inferior, especially after the late 19th century immigration to the States. Jews today in the US are usually "white" by someone else's categorization. But after blacks, Jews are still the leading target in the questionable FBI database on hate crimes IIRC.
To give a tortuous demonstration of my point, Luis Wacquant (also interviewed on Lilley's show by the cohost IIRC) recently argued that the imprisonment wave in the United States is a heavily racialized phenomenon of state power in the Focaultian sense of "sovereign power" over the body (prison) and over family (kids without dads, though I want to be careful with that statement) with a strong element of economic discipline. He says in no uncertain terms that punishment is a clearly racialized phenomenon. Likewise Sonnie and Tracey suggests that the reactionary backlash by working-class whites was strongly motivated by race, and of course there's Calhoun and about two hundred years of scholarship obsessed with "race" and tracking down the One True Aryan Bloodline of Europe and the Mid-Atlantic American States or whatever. But Wacquant outlined several specific ways to address the prison problem, and *every* single one of them was a policy suggestion largely devoid of racial content (This recalls the fact I've seen cited in a number of places, that upon controlling for income in the prison population, whites are no longer over-represented. I have to question that data in light of other points, like Wacquant's on the lowering rate of violent white offenders actually incarcerated since the 1970s vs. increased reports of violent acts by whites). I guess this puts me on the Henwood/Reed part of the spectrum here. The things necessary to help blacks in the US are also going to help a large segment of people of different perceived skin tones, etc.
None of this is to disagree with Carrol's points, but I would suggest that (3) is a lot like the '70s-era politics of leftist groupuscles separated by subjectivities in order to be effective--unless Carrol is suggesting that in a much more vernacular, i.e., everyday way, like how individuals in neighborhoods tend towards certain obvious class and race similarities, so whatever groups rise from them would be contingently homogeneous but not so out of theoretical necessity.
Apologies for the name-dropping blather, neologisms and other poly-syllabic words.