Ethnocentrism can (but does not have to) negate the possibility of cross cutting cleavages. You can argue that our party politics would look different if we had more cross cutting cleavages and less ethnocentrism in the US.
When a group feels strong ethnocentrism, its ethnicity becomes its most relevant characteristic. In such cases, it will not be affected by cleavages that are based on things like economics or religion.
You can argue that the Republican Party has become the party of ethnocentric whites, unable to reach out to blacks and Latinos on cultural issues, especially. You can argue that the Democratic Party has become based on minority groups and has a hard time reaching out to whites.
Outside of partisan politics, you can see that many of our economic issues have come to be seen as racial issues and so have issues of crime.