The First International was dominated by a vicious debate between Marx, who advocated State Socialism, and Bakunin, who advocated a type of Anarchism. It should be noted that Bakunin predicted with startling accuracy the degeneration of Revolutionary Parties that stood for election into reformist parties, as well as the horrors of the Soviet Union during the course of these debates (which were in the 1860s).
Obviously in OTL, Marx won and got Bakunin kicked out of the International. What would be required for Marx to be kicked out instead, and what effect would such have on the world wide labor movement?