I am not a big fan of the word 'must', but there are several areas that 'should' be covered, most of them originating with my discipline, anthropology: Cultural relativism, cultural variability, similarities across cultures - Don Brown's "Human Universals" is an excellent source for this argument, that 'race' genetically does not exist - there are numerous sources in support of this as it is a cline biologically.
As for courses obviously I would recommend anthropology, more than one course. In addition to intro an area or culture specific course is highly desirable. Human geography would also be helpful, as would be human ecology.
This is not an exhaustive list but I don't believe that is what you are seeking.
The key concept is "CULTURAL SAFETY" - as humans we can never know everything about another individual/culture. However, if we approach each situation with humility and curiosity we can begin to have discussions which will enable us to acquire the knowledge necessary to treat each other with respect and dignity.