Humans are psychologically predisposed to forming in-group and out-group thoughts. If there are racial differences in a society then race will be one of the factors that determines 'otherness'. If race is not a factor, it'll be something else. See the Rwandan genocide, the Holocaust and the eradication of the Hugenots for example of 'othering' where skin colour was not the main determining factor.
In a multicultural society you can expect race to be determining 'otherness' factor in the thought process of the population. This is because it is usually very easy to distinguish. This is true of all cultures and across history. The trick is to ensure that this thought process doesn't inform the legal structures of a pluralist society and to ensure that you attempt to mix people of different ethnicities together to form community cohesion - that takes time. That's something that needs addressing in the west, though it is particularly pronounced problem in the USA and South Africa. It's not a quick fix. Racism has to be tackled at the individual level through mixing, and at the group level through legalistic advocacy and careful planning. That's the trick
The less effective trick is to try and erradicate it by encouraging everyone to yell contradictory messages at each other until everyone has stopped listening or died of fatigue. That's currently the plan and it isn't working.