The New York Times provides an illuminating graph showing the respective racial-ethnic proportions of the Democrats, Republicans, and the overall U.S. population.
Per the Census Bureau, the racial-ethnic composition of the U.S. population was thus in 2010 (at least for the four biggest groupings):
White, non-Hispanic: 63.4%
Republican districts, per the Times, are significantly whiter and less racially-ethnically diverse than Democratic districts. In the red (Republican) districts, whites make up nearly 75% of the population. Whites are 51% of the population in the blue (Democratic) districts.
The racial-ethnic demographic disparities are also found among Hispanics, Blacks, and Asians. For example, Hispanics make up nearly 23% of the population in Democratic districts, but only 11% in GOP districts. Blacks, in turn, constitute 16% of blue districts, but only 8.5% of red districts. Asians compose nearly 7% of Democratic districts, but only 3% of GOP districts.
The bottom line is that overall, Democratic congressional districts reflect the racial-ethnic diversity of the U.S., while for the most part, GOP districts do not.
The graph is linked below.
New York Times: Red vs. Blue Congressional Districts in Terms of Racial-Ethnic Composition