How did Italian Americans react to the U.S. being at war with Fascist Italy during WW2? Was there any widespread support for Mussolini among Italian Americans?

A recent historical monograph about this topic has been written by Katy Hull under the title The Machine has a Soul: American Sympathy with Italian Fascism, published by Princeton University Press in 2021.

Mrs Hull names Mussolini and Fascism: The View from America (1972) by John Diggins as the most complete forerunner to her own work, but I don't have access to this book myself.

Regardless, Hull roughly divides the United States' general relationship (not yet specifically constrained to Italian Americans) into the following phases:

Initial sympathy with the emerging fascist movement, which was perceived as philosophically rejuvenating in nature and which had the aesthetic of physical and mental renewal of America's former ally during the war years.
Considerable admiration, especially after 1925, for Benito Mussolini as a person, especially as a headstrong decision maker not bound by the political squabbling and the constrained overton window of liberal democracy and particularly the American two party system. Hull characterizes Mussolini as befitting of the 1920s American desire for singular strong men to provide leadership during an ever more confusing modernizing world.
Exploding growth in desire for a more state-guided socioeconomic and political model, at least under the purview of a stronger and more personally identifiable leadership, during the timeframe of what Hull calls the "era of democratic disillusionment", i.e. the immense frustration felt by the American lower and middle classes during the Great Depression after 1929. This coincided with the high tide of American desire for "populist" (though only rarely "fascist") politics, and populists who emerged as prominent American political figures in the next few years included Huey Long, Upton Sinclair, Francis Townsend and Charles Coughlin.
Support for Mussolini, both within and without Italian American circles, was not limited to the conservative population, and even American liberals (even though typically only whites) at times appreciated Mussolini's government (albeit for different reasons than American conservatives).
Gradual lessening of the frustration with lack of American personal leadership after the election of Franklin D. Roosevelt, whose more charismatic style and self-stylization as a crisis solver made him more appealing than his predecessors Calvin Coolidge and Herbert Hoover. FDR and Mussolini were often compared, and observers in the United States often found similarities in their personalities.
Growing hostility after the mid-1930s, especially after the 1935/1936 Italian invasion of Abyssinia (Ethiopia), peaking after the 1939 Invasion of Albania and the 1940 Italian entry into World War II. On 11 December 1941, Italy declared war on the United States.

Do note that the cultural trends mainly affected White Americans, and that especially African Americans took a much more nuanced and skeptical stance much earlier, and a considerable number of African Americans even volunteered to serve on the Ethiopian side of the 1935/1936 war against fascist Italy, even though most (but not all, see John Robinson, "father of the Tuskegee Airmen") were prevented by the U.S. government from participation in the conflict.

Let's talk about the specific role of Italian Americans then.

Italian American feelings towards fascist Italy were usually quite positive after his takeover in 1922 and even after his dictatorial assumption of powers in 1925. This was further strengthened by the usually socially most influential part of Italian American life - the Catholic clergy - after the Italian concordat with the Papacy in 1929, creating Vatican City as a country and ending the conflict between the Popes and the governments of Italy which had begun in the 1860s.
White nationalism and white supremacy did not yet exist in the United States in the exact same form as we see today, which we might think of as "pan-white". Back then, white supremacist groups (most notably the second generation of the Ku Klux Klan) were still much more dominated by a focus on the ethnosocial group of the WASPs (White Anglo-Saxon Protestants), and views of southern Europeans as racially inferior, as well as views of Catholics as religiously inferior, were widespread among some parts of the White American population. Italian Americans were thus less closely intertwined with the United States and had a stronger persistent connection to the Italian homeland, resulting in a stronger likelihood to also hold a desire to identify with the Italian political leadership.
Mussolini was attractive to Italian Americans because of the prospect of a restored national pride that was already inherent among other White American groups because of their respective homeland's successes. Fascism as a totalitarian ideology with its inherent and widely propagandized dynamism also offered a counterpoint against dominant American cultural stereotypes, especially held by WASP ethnonationalists (see above), of Italians as anarchic, boring, non-vitalist, prone to criminality, and lazy.
Several powerful social institutions within the Italian American community became covert or even overt sympathizers of the fascist cause. The largest Italian-language newspaper in the U.S., Il Progreso Italo-Americano. was acquired by one Generoso Pope in 1928, and he continued the newspaper's previous pro-fascist and pro-Mussolini reporting, amplifying it with the investments of additional funds. Pope was a conservative Democrat, and advocated his readers to vote for the Democratic Party. FDR, among others, sought and received positive coverage in Il Progreso. Pope even extended the newspaper into an English-language section to more effectively approach second-generation immigrants and non-Italian Americans.
Italian Americans were called upon by pro-fascist elements to donate to the war effort in Ethiopia, in what was explicitly framed as an effort to assist the Italian homeland in breaking free from the League of Nations. Stereotypical of the period became the Italian American depictions of Italy (and Ethiopia) as "gardens" to be fostered from far away so they could blossom in the distance to assist the Italian people and the relatives of Italian Americans who had remained behind.
After the birth of the Axis Powers with the "Pact of Steel", Italian American groups at times cooperated with German American pro-Nazi groups, like the German-American Bund, for example in the opening of Camp Nordland in New Jersey.
Italy's growing association with Nazi Germany, and the Italian adoption of the first Nazi-style racial laws targeting Jews (in 1938), increasingly ostracized Italian Americans from larger American society, and ethnic tensions grew especially between Italian Americans and two other groups: African Americans, who were widely sympathetic to Ethiopia (Africa's last uncolonized land in 1936), and Jewish Americans, who despised Nazi Germany. Mutual calls for boycots were frequent, and pro-Nazi German Americans attempted to, in solidarity with pro-fascist elements of Italian Americans, organize large scale boycots of "Jewish finance".
With the growth of this ethnic tension began a notable growth of anti-fascist tendencies within the Italian American community and the growing division even within local communities and families over political allegiance to Italy versus political allegiance to the United States and to its various constituent parts who were ethnically at odds with fascism.
The Italian American opinion of Italy became less and less important to the government in Rome over time, as foreign minister Ciano after 1938 favored a solid relationship with Nazi Germany over the game with American public opinion. Warnings by Italian American leaders, especially Pope, that continued antisemitic policies in Italy would irritate Italian American sentiments further had no impact upon the pro-Nazi course of the Italian government.
Public opinion in the United States (at large, not just Italian American) was decisively more germanophobic than italianophobic in 1938, but continued association of Italy with Germany also decreased Italy's standing over time.
Italian American opinion was still largely pro-Italian on 10 June 1940, when Italy entered World War II. FDR's speech about Italy as "the hand that held the dagger" (referencing Italy's invasion of France) was not appreciated. Nonetheless, FDR continued to utilize Pope and his Italian American newspaper for Democratic campaigning in both 1940 and even in 1944.
The increasing conflict of Italian Americans between their Italian identity and the identity as "loyal Americans" who desired equal standing among America's ethnicities (or, to be more precise: America's white ethnicities) inevitably broke into an identity crisis with the American entry into World War II. The resulting discourse was a mixture of denial (Il Populo claimed that it had "consistently and vigorously denounced Mussolini and his fascist courses", a claim that is both hilarious and hilariously false) and ideological bargaining (the idea that "true fascism" of the Italian kind had stopped existing in Italy after the adoption of antisemitic legislation in 1938, and that post-1938 Mussolini had been more a German puppet than a genuine Italian fascist).
During World War II itself, Italian Americans served in the U.S. military with no particular lack of distinction, including in the Italian theater.
At the Italian American homefront, positive conversation about Mussolini (now the enemy) was tabooized, but nostalgia for "genuine Italian fascism" (again under the idea that post-1938 Italian fascism had betrayed the movement's routes as well as the Italian concept of nationhood) probably remained.