In Germany, the split between radical, communist socialism and more moderate, democratic/parliamentarian socialism can be traced back all the way to the differences between Marx and Engels on one hand, and Ferdinand Lassalle, founder of the Allgemeine Deutsche Arbeiterverein (ADAV, "Universal German Worker's League") on the other, with Lassalle favoring a more moderate, reformist approach to socialism.
The ADAV would eventually come to be one of the founding elements of the German Social Democratic Labor Party (SDAP), and the party's 1875 Gotha Program already was very strongly directed towards reformism and parliamentarism as methods to achieve a socialist society. For that, it was strongly criticized by Marx in his Critique of the Gotha Program (1875/91).
So at least German social democracy has always contained a strong non-revolutionary (if not anti-revolutionary) wing.
This would become even more pronounced in 1917, when anti-war socialists split off from the mainstream Social Democrats and founded the USPD. Elements of the USPD and other leftist groups would eventually form the Spartakusbund and attempt to spark a socialist revolution in Germany in November 1918, right at the time when mainstream Social Democrats under Scheidemann had become part of the Imperial German government for the first time in history, and had just proclaimed the Weimar Republic.
The Spartacists were eventually put down with support of the mainstream Social Democrats, their leaders shot by right-wing paramilitaries. Some survivors would remain to form the Communist Party of Germany (KPD) which would eventually develop strong ties to the Russian Bolsheviks.
At that point, I think we can say the German Social Democrats had definitely split from revolutionary socialism.
The major steps of separation were linked to the Russian revolution; either because of the October revolution (split between Mensheviks and Bolsheviks), or because of the founding of the Third International (Comintern). For example in France, the founding moment of social-democracy is the congress of Tours (1920) that saw the separation between the Communist Party, which joined the Comintern, and the SFIO, which remained a member of the 2nd International. In particular, Léon Blum was hugely influential in defining the social-democrat doctrine in France (and maintaining a cadre for the rump, minority SFIO).