Most sports reduce discrimination and division, I think.
Side-tracking people into unimportant (sports) in-group versus out-group is really good at improving cohesion between important group differences. For example a Mexican and an American rooting for the same team, so they have their sport in common, which helps them be closer to each other.
Sports can be divisive between countries. Then again it is interesting to watch New Zealand support Australians against the English (background - there is usually strong sports rivalry between NZ and Oz since we are neighbours). A bit of win and lose on that one.
The most popular sports tend to be cross-class too - which is good. Of course there are sports that tend to be class oriented in some countries e.g. polo, soccer, athletics. FYI golf and skiing are not particularly class oriented within New Zealand: even 30 foot yacht racing can have a mixture of millionaires, factory workers, professionals and petrol attendants (we are weird down here).
Just a theory of mine.