German Nazism was much more extreme than Italian fascism in a lot of ways, and even though Mussolini was anti-semitic himself, Italian fascism as a whole wasn’t, and there were actually a bunch of Italian Jewish fascists in the early party. In fact three of the fascist blackshirts who were killed in the early fights with Socialist and Communist gangs, Gino Bolaffi, Bruno Mondolfo and Duilio Sinigaglia, were all Jews, and about 200 Jews participated in the march on Rome.
And there were Jews in the Fascist Italian government. Aldo Finzi, one of the members of the first Fascist Grand Council was Jewish, as was Dante Almansi, Vice Chief of Police, Guido Jung, the Finance Minister from 1932-1935, and Maurizio Rava was the governor of Somalia. One of Mussolini’s mistresses, Margherita Sarfatti, who was also active in “legitimizing” Fascism, was Jewish.
The Italian government didn’t really become anti-semitic until after the invasion of Ethiopia, when they were condemned by the League of Nations, and Germany was really their only choice as an ally. At that point, the government realized it would have to make concessions to German attitudes and moved to a more anti-semitic policy.
But if you look at the situation, Italy became fascist in 1922. It wasn’t until 1938, 16 years later, that it passed the “Laws for the Defense of the Race”, which forbade Jews from going to public schools, banned marriage between Jews and non-Jews, banned Jewish ownership of land, kicked Jews out of the army and civil service, and so on. Compare that to Nazi Germany where the Nazis took power in 1933 and passed the Nuremberg Laws in 1935, just two years later.
The other thing to remember was that the Nazis in Germany had substantially more public support than the Italian fascists.