I think it means the usual meaning. The greater context of your text may explain the contention or dispute -- that is, the degree to which the 'contention' may have intensified to a 'dispute' with specific personalities...

“This was Macke's second journey to Paris - the first, in 1907, reflected less the contention/dispute with the avante-garde than, above all else, his encounter with the works of Manet as well as those of the later Impressionists."

See this:
http://www.metmuseum.org/toah/ht/11/euwcm/ht11euwcm.htm

"1905 Die Brücke (The Bridge), a group of painters and printmakers who contribute to the development of Expressionism, is founded in Dresden, continuing there and in Berlin until 1913. Members include Ernst Ludwig Kirchner (1880–1938), Erich Heckel (1883–1970), and Emil Nolde (1867–1956). Unlike the French avant-garde, Expressionists privilege the artist's inner emotional state, focusing on the anxieties of modern life and taboo subjects such as sexuality, expressed in bright, unnatural colors and distorted forms."

This refers to Macke's analysis of the work of the avant-garde.

Auseinandersetzung is dispute/contention.
Internet in French has short biographies of Macke and it is not sure that he really had a dispute with the "Avantgarde", but definitely that he was impressed by Manet and the later impressionists.
So perhaps something more subdued might fit the context better.