Its hard to give a firm answer because the states of Italy and Germany changed their stances on the Bolsheviks depending on what was more politically advantageous at the time.

The Nazis believed that the entire Russian Revolution was a Jewish conspiracy to help establish the Zionist Occupation Government. Nazi antisemitism was heavily influenced by the propaganda and beliefs of the anti-Bolshevik White movement. The infamous The Protocols of the Elders of Zion is of White Russian origin, and was distributed by Russians living in exile. Notably in Germany and the United States. Dietrich Eckart and Alfred Rosenberg, both major influences on Hitler and the Nazi Party, were ardent proponents of The Protocols. Eckart published it in his newspaper Münchener Beobachter, which became the major Nazi newspaper until the end of WW2.

Lenin and Trotsky, along with Jewish revolutionaries like Julius Martov and Emma Goldman, were depicted in Nazi propaganda as important leaders in the Judeo–Bolshevist conspiracy. It did not matter that Lenin was only faintly Jewish, and was not aware of his ancestry. Nazi Germany, at least in official state propaganda, was more receptive to Stalin than Trotsky or Lenin. Stalin's own antisemitism and hostility towards Trotsky meant that he could be portrayed as a mutual ally of the Nazis in the fight against The International Jew.

Officially, Fascist Italy adopted the same stance as Nazi Germany. Before their alliance, Mussolini made contradictory statements about Jews and the Bolshevik leadership. At times he praised the Soviet Union and compared himself to Lenin, but also propagated the Judeo-Bolshevik conspiracy. The Fascists were threatened by the Bolshevik alliance in the political struggle over Italy, but did not view it through the racial lens that Germany did. Once allied with Nazi Germany, the Fascist state adopted the Nazi doctrines of antisemitism and anticommunism.

Sources:

Russia and Germany: A Century of Conflict by Walter LaqueurLenin, Stalin and Hitler: The Age of Social CatastrophePariahs, Partners, Predators: German–Soviet Relations, 1922–1941 by Alexander NekrichBolshevism from Moses to Lenin by Adolf Hitler and Dietrich Eckart (not that I agree with them in any way, but it does outline their views of Lenin and Judeo-Bolshevik conspiracies)