To assert that whites don't think in racial terms and non-whites do is hardly novel in the Steveosphere, but the narrative that holds white racism to be ubiquitous and oppressive relies on the assumption that whites are racially conscious.
There is little evidence for this assumption. The GSS asked respondents to choose the three most important ways they self-identify from a list of ten descriptors. One of these was by racial or ethnic background. The graph shows the percentages by race of those who included this among the top three most important methods of self-identification:
The sample sizes for Hispanics (37) and Asians (44)* are small, but the pattern is clear. Only one out of ten whites included this among their top three. Among non-whites, about four out of ten did.
Since minorities are by definition not in the majority, it is expected that a distinguishing attribute will be deemed more important by the minority than it will be by the majority. The option combines race and ethnicity, though. When whites are broken down by ethnic group, only those of German descent constitute a larger American population than blacks do. But it's not just race that whites ignore. They don't think in ethnic terms, either.
As the percentage of the population that is white continues to shrink, white racial self-awareness will increase. This question set was only posed in 2004, so it's not possible to gauge the change in self-identification over time, but just looking at different age generations bears this out. By age range, the percentage of whites who include race or ethnicity among the top three ways they identify themselves:
A colorblind society is a society in which everyone is the same color. Diversity leads to more racialism. Those who relentlessly promote it should be asked to explain why they support increasing the amount of racialism in society.
GSS variables used: RACECEN1(1), SOCID1, SOCID2, SOCID3, AGE(18-29)(30-44)(45-64)(65-89)
* Hispanic also includes "some other race", as it is a method of racial identification used almost exclusively (97% of the time) by Hispanics. The Asian category includes Indian, Chinese, Japanese, Filipino, and "other Asian".