BYU is not a culturally diverse campus. The majority of students are white, middle-class Mormon kids. However, it is unlikely that you will go the length of your college career without meeting someone from another country. BYU has a large number of countries represented at the University.
There is also added diversity in the fact that over half of
the students have spent significant time outside of the
United States. It is not uncommon to walk around campus
and hear the boy from your psychology class calling to a friend in Hungarian. So, while the student body is pretty homogenous, you can still have a very diverse experience