That’s a good question. There were fascist Zionists, and there are certainly neofascist strands in Zionism today, but it is an exaggeration to refer to Zionism per se as fascist. Rather, Zionism is colonialist, just like Fascism was. Fascism was the militarist, predominantly petty‐bourgeois movement that the haute‐bourgeoisie promoted to institutional power in order to strengthen capitalism, which involved eliminating the proletariat’s concessions. Colonialism was also part of the job, though, as the Fascists inherited a colonial empire and were outraged when the Entente failed to give the Kingdom of Italy more land as reward for helping win WWI.

Zionism emerged from the same soil, not just geographically but also in terms of how it likewise recommended colonialism by any means necessary. It was (and still is) a capitulation to antisemitism: the Zionists believed that Jews and gentiles were incompatible, so separatism was necessary and Jews had to settle in Patagonia, Uganda, or Palestine. The Zionists wanted a formidable neocolony, but not necessarily a superpower that could compete with other empires.

Compared to the Fascists, who were adventurer‐conquerors, the Zionists were and still are much less ambitious. As far as I know, the Zionists haven’t tried to extinguish class‐consciousness through a merciless crackdown on proletarian organizations either (unless the organizations were Palestinian).

That said, the régime has been unafraid to grant neofascists some political power (similar to how the Kingdom of Italy and the Weimar Republic allowed fascists in parliaments), and early on it did receive support from the Fascist empires, so I think that it is at least easy to understand why people consider Zionism per se fascist even if it be an exaggeration. For now, I believe that ‘parafascist’ would be an accurater description of the neocolony.

Zionism is colonialism. Fascism is distinguished by Europeans for when colonialism returns home and infects them.

Zionism predates fascism, but they're inextricably intertwined ever since the Haavara Agreement.

The Haavara (Transfer) Agreement, negotiated by Eliezer Hoofein, director of the Anglo-Palestine Bank, was agreed to by the Reich Economics Ministry in 1933, and continued, with declining German government support, until it was wound up in 1939. Under the agreement, Jews emigrating from Germany could use their assets to purchase German-manufactured goods for export, thus salvaging their personal assets during emigration. The agreement provided a substantial export market for German factories in British-ruled Palestine. Between November 1933, and 31 December 1937, 77,800,000 Reichmarks, or $22,500,000, (values in 1938 currency) worth of goods were exported to Jewish businesses in Palestine under the program. By the time the program ended with the start of World War II, the total had risen to 105,000,000 marks (about $35,000,000, 1939 values).

Emigrants with capital of £1,000, (about $5,000 in 1930s currency value) could move to Palestine in spite of severe British restrictions on Jewish immigration under an immigrant investor program similar to the modern United States EB-5 visa. Under the Transfer Agreement, about 39% of an emigrant's funds were given to Jewish communal economic development projects, leaving individuals with about 43% of the funds.

The Haavara Agreement was thought by some German circles to be a possible way to solve the "Jewish problem." The head of the Middle Eastern division of the foreign ministry, the anti-Nazi politician Werner Otto von Hentig, supported the policy of settling Jews in Palestine. Hentig believed that if the Jewish population was concentrated in a single foreign entity, then foreign diplomatic policy and containment of the Jews would become easier. Hitler's own support of the Haavara Agreement was unclear and varied throughout the 1930s. Initially, Hitler seemed indifferent to the economic details of the plan, but he supported it in the period from September 1937 to 1939.

It seems like the fascists tried to speedrun the US’s success as a rival imperialist while Israel is simply an extension of the US’s power using the same settler colonialism. While the fascists were ambitious and trying to revive an imperialist past, the Zionists have less history to rely on and are simply an extension of existing imperialism rather than trying to rival it. That’s just some random analysis of the differences. They are largely similar, but other people have better reasons they are different.