I think that any time you can get people to see others as PEOPLE, minus the “different from me” label, you go a long way in closing the gaps you discuss.
Would intramurals be one approach? Sure, if you can get a variety of kids to come out for them. Personally, they wouldn’t have been my cup of tea.
But any sort of activity that brings different people together, that lets them see the strengths and similarities of people they might otherwise not have come to know, should help bridge the gaps.