Racism will exist as long as there continues to be different ethnic groups. The only way to eliminate racism would be either to have full integration so there is no concept of a 'minority' or a 'majority' group... or to make everyone the same race. Genocide would be a valid (if violent) way to promote the latter option, but enough sexual mixing between different ethnic groups will lead to many people having a combination of racial traits - if this continues for long enough, it doesn't seem unlikely that most people in the world will be what we'd currently call 'mixed race'. The former option is probably impossible because of racism itself.
The reason I say racism is inevitable when there are ethnic minorities is because when people have little experience with other races, they'll base their perception of a particular race on a limited sample size - if all their encounters with other ethnic groups have been negative, then clearly they'll have a negative perception of that ethnic group. Racism can only be combatted through exposure to other ethnic groups from one's own.