It won’t get rid of color based racism (think about Apartheid in South Africa, where a white minority ruled over a much larger black majority. The reality is that there is plenty of inter ethnic tension and bias, a local town had an area that historically was black dating back to the revolution, and in the last couple of decades with the influx of Mexican and Central American people has caused major friction between the two groups, much of it ugly and racial. In the 19th century, the first major influx of Jews were from Germany, when Russian Jews came in the late 19th century the German Jews looked down upon the newcomers, as being ignorant peasants, etc…
Racism might be more compartmentalized in a society where no one group is the majority. In recent times, some towns in NJ and NY state have become hotbeds of controversy as they became hubs for Hasidic Jews and they came to become a majority, and the Hasidim took over local government and did things that others felt were discriminatory, like slashing spending on public schools (and often openly arguing that since their kids didn’t use the public schools, they shouldn’t have to pay such high taxes), this was especially true in towns like Lakewood in NJ where the public schools tended to be kids who were of black or hispanic background…and similar things have happened elsewhere, complaints of anti white bias in areas dominated by other groups. The thing to keep in mind is that even if the country is no longer a majority anyone, locally you still can have imbalances thatg cause problems, too.