Square Dance Story is a short fictional movie (14 minutes) that features square dancing. It was made in Canada (specifically in British Columbia) in 2011. There is no dialogue in this movie, and the only speech that is understandable is the square dance calls.
An outsider enters a strange bar hoping to connect with people and instead finds a curious square dance troupe in the back. In the troupe, he pursues a mysterious square dancer only to be chastised [by her] and the square dance caller steps in order to save the troupe from fragmenting.
The square dancing seems legitimate (although the calls and what the dancers are doing in the shots do not always match), so this instance of square dancing appearing in popular culture will not be given the ignominious label of “not quite right“, unlike the vast majority of other instances.