Certainly, if one grows up under an authoritarian household and does not rebel against the teaching of the house, that person may end up more likely to hold authoritarian and prejudiced views. However, there are many examples of people who grew up in incredibly authoritarian and racist households who rejected the teaching of their parents or guardians. For example, there is a particularly strong trend of southern children of racists growing up to be anti-racist and anti-authoritarian. Of course, on the flip side, if people do not actively reject this conditioning, then intergenerational cycles of abuse will continue.
If I received this assignment, I would certainly research the United States government as an example of an authoritarian state that has, since its genocidal founding, enacted a divide-and-conquer strategy of control over its subjects through creating and bolstering racial division and hostility. I would definitely research how laws were created in the colonies that outlawed interracial relationships and bolstered divisions between indentured European servants and enslaved African people in order to ensure that the two groups would not rise up together against their common oppressors. This divide-and-conquer strategy continues today through, for example, state propaganda that encourages white Americans to blame immigrant people of color for financial problems that are, in fact, the fault of US policies and capitalist greed. This divide-and-conquer strategy continues to ensure that people will not come together against a common oppressor and will, instead, fight amongst each other and actively contribute to racist oppression.