It is disingenuous to claim that race does not exist. Races are categorizations of people based on superficial physical appearances such as skin color. To say otherwise is to hide from the inherent problems.
To base opinions and decisions on race is not fair or intelligent because every attribute[1] of the person has more variation within the category than between categories, whereas racism tends to treat race as an entirely homogenous category.
To make matters significantly stickier(?) there is a high correlation between race and culture. I suspect that many race issues are really clashes between cultures. See: UTism
[1] Except possibly the superficial physical attribute used to make the categorization in the first place.