Oh, there can be no doubt of the controversial nature of Courbet's work on two fronts: depictions of rural life and of the erotic. Let's discuss each of them in turn.
At the time in France, depicting the working class in artwork was considered inappropriate. Highlighting the everyday activities of those who would be considered "poor" even more so! Probably the best example of this is Courbet's The Burial at Ornans which depicts a common peasant burial in France. In addition to the fact that the lower class is represented, there is no real sadness is apparent in the work that focuses only on caricatures of the subjects. As a result, many critics called it simply "ugly." As one art historian admitted:
In Paris the Burial was judged as a work that had thrust itself into the grand tradition of history painting, like an upstart in dirty boots crashing a genteel party, and in terms of that tradition it was of course found wanting.
But there can't be a discussion about Courbet's controversial nature without talking about his more erotic works. A painting (Sleep) of two women in bed together, buck naked, was simply unheard of in the art world at the time. Again, one must discuss here Courbet's most significant work: The Origin of the World which very realistically depicts a graphic view of female genitalia (both ironic and a tad humorous).
As a result, Courbet doesn't fit well into any of the artistic schools in France at the time (i.e. he is considered neither part of the Romantic nor part of the Neoclassical movement). In fact, Courbet himself admitted the following:
The Burial at Ornans was in reality the burial of Romanticism.