This mostly answerd your "threshold question" and a stab at why "Italian Anarchists" made it into popular understanding. I do study anarchist history but am not deeply focused on Italian immigrants, so if interested in more exploration of the particular attraction of anarchism in that context it will have to wait until its not the middle of the night!

While most Italian immigrants werent Anarchists, it would probably be fair to say it was the dominant tendency among "left wing" Italians in the US during this period, and were a visible and sometimes significant presence in local communities for several decades. Kenyon Zimmer argued in the intro of Immigrants Against the State: Yiddish and Italian Anarchism in America that "Anarchism would be the dominent radical ideology among Jewish immigrants until the mid-1890s, among ethnic Russian and Asian immigrants until the 1920s, and among Spanish, Mexican, and Italian immigrants into the 1930s." As an imperfect illustration, in 1912 the Italian Anarchist press had a combined circulation of around 10,000, above the 6,500 claimed by the three papers of the Italian Section of the Socialist Party that year.. So if you were an Italian immigrant stonecutter in the granite quarries of Barre, Vermont or a silkweaver in Paterson, or a baker in San Francisco, or a dockworker in New Orleans its quite likely that when you and your coworkers were forming a union that anarchists were heavily in the mix as agitators and organizers. If you frequented a workingmans saloon the guys shouting over each other about politics probably had an anti-authoritarian, anti-state, anti-clerical bent to their jabs. If you went to the big radical picnic on the outskirts of the city, it was probably put on by Anarchists.

As mentioned above, Anarchism was the most prominent radical tendency, and thus a frequently visible force, within many immigrant communitites. For some of the deeper-rooted milleus, such as that among Spanish and Italian immigrants, this history could be traced in part to long-running history of Anarchism in their countries of origin. The "Anti-Authoritarian" wing of the 1860s-70s International Workingmans Association was strong in many countries and laid the foundation for a longstanding Anarchist movement. Thus there were a large number of anarchists in Italy among those traveling to the US (and elsewhere... Italian immigrants were prominent among anarchist communities from Cairo to Buenos Aires). Being an anarchist agitator is and was a dangerous thing in most places, and many Italian Anarchists had to leave both for political and economic reasons. On the other hand, the experience of brutal work and discrimination from wider society upon arriving in the United States radicalized many immigrants towards Anarchism.

A few events following World War I probably helped cement a visible role for Italian-American anarchists in broader historical memory around early 20th century labor struggles. Amid the First Red Scare following World War I, in which hundreds of anarchists and labor agitators were deported (Italiand making up a large chunk), a wave of bombings struck targets including Wall Street and the home of Attorney General A Mitchell Palmer (who oversaw the state repression campaign). It is generally believed many of these bombings were the work of the circles around anarchist Luigi Galleani. Amid this, two Italian Anarchists, Nicola Sacco and Bartolomeo Vanzetti, were arrested in Massachussets on charges of robbery and murder. Their case, widely believed to be a frameup-job, became a years long international cause-celebré taken up by groups from the Third International to the young ACLU before they were executed. The case has been memorialized in song and even occasionally makes it into school history curriculum.

Basically you're asking for a brief history of left movements in Europe around the turn of the century. Let's start.

First of all, there were not actual communists before Russian revolution in 1918. Yes, communism, i.e. a society without classes, was the utopian goal of many socialist movements, but there weren't communists as a separate faction than socialists. Communist parties were born after Russian revolution from that part of socialists that wanted to "make like in Russia", meaning a violent revolution.

So, before the Great war the left is divided in two main factions: socialists and anarchists. There were many different movements in these, violent and peaceful, reformer or revolutionary, but let's stay straight. Basically socialism was a laboring movement, popular into factories, and anarchism was more spreaded in countryside between farmers and serfs.

Geographically, socialism was stronger in heavily industrialized countries like Germany, France and Great Britain. Anarchism was stronger in largely rural countries like Spain, Italy and Russia. That's why many Italian immigrants were anarchist.

Anarchists were more flamboyant too. Between the two centuries, the reformist faction was the main one within the socialists. And even the extreme faction did not talk about "all power to the soviets" and killing all the bourgeoisie, this would happen after the Russian revolution, but rather about general strikes, pickets, worker-owned factories...

On the other hand a relevant part of anarchism sought to make society crumble through targeted killings or even terrorist attacks. An Italian king, a Spanish first minister, a French president and the famous Austrian princess Sissi were all killed by Italian anarchists before WWI. After the war, in 1920, an Italian anarchist, Mario Buda, was the inventor of the car bomb for an attack in Wall Street (40 dead).

So, answering your question: anarchism was actually more attractive for Italians and Italo-americans around the turn of 20th century. Also, anarchism was more violent at that time and is therefore more remembered.