From what I've found - and again there is practically no literature on the subject outside of the aforementioned neo-Confederate revisionist nonsense that makes hay out of the matter - socialist identification directly correlated with Republicanism anywhere there was a large German immigrant community, and, though I have no hard numbers, the impression I get is that most German-American Republicans in the first generation of immigrants during the Civil War period had socialist leanings.
Now, this holds good for Ohio and the upper Midwest. I've been curious about self-identified socialist immigrants to New York City, many of whom may have been Fenians and as such much more sympathetic to the Democratic Party. But the Fenians were not strict socialists, and what socialists were among them likely would not have been 'scientific'.
First off, welcome!
Second, yeah Fenian revolutionaries, Land Leaguers, and other Irish Nationalists were strongly Democratic. This had a long political tradition that went to long before the Civil War Era to the First Party System when many Irish immigrants strongly identified with the Democratic Republican cause due to natural opposition to the Federalist cause. The Alien and Sedition Acts along with the Naturalization Acts passed in the late 1790s contained not only strong restrictions against French aliens, but Irish ones as well. Harrison Gray Otis, a well known MA Federalist, cited his not wanting "wild Irishmen roaming the country" as a chief reason why the Congress at the time should pass the Acts. The Irish (both protestant and catholic) responded in kind by strongly backing Jefferson and his ideological successors. I should also note that many of the survivors of the Irish Rebellion of 1798 were also adamant Jeffersonians once in America, often advancing the case for voter suffrage and other liberal causes of the time.
So yes, even before Andrew Jackson (emphasis) there was a strong Democratic tendency among the Irish in America. The Alien and Sedition Acts were arguably the "Original Sin", if you will. Opposing popular suffrage and supporting moral regulation like Temperance also didn't help National Republicans and Whigs with the group. By the time the GOP came around, it would've been easier to convince many an Irishman that he could walk on water than to disavow his Democratic allegiances. There was one Irish Republican who had links with Nationalism, John Conness, who started out as a "War Democrat" from California who was later kicked out of his own party due to his extremism on Civil Rights and rights for immigrants, including the Chinese who were very unpopular in California.
By and large though, a vast majority of them were on the opposite fringe of the Democratic Party from white landowners in the South. For obvious reasons. The two groups didn't have much in common except a distrust of Republicans and non-whites, for similar yet different reasons. What a white Democrat from the South saw as a threat to his monopoly an Irish one would see a threat to his survival, if that makes sense. This explains a lot of the unfortunate racism in the early labor unions, as many of the Irish laborers saw minorities like blacks and the Chinese essentially being "scabs" for the Robber Barons who they and other European ethnic groups involved in labor were at war with. If you want to go even further, many of the working class Irish (but not the lace curtain classes that were prominent businessmen who controlled machines like Tammany in the late 19th century) viewed themselves in a sort of centuries long cultural war with all things English and were convinced that the economic troubles they faced in the New World was the result of an ingrained Brahmin elite that was deadset to make sure they stayed second class for another hundred years (I can't say I disagree too much with that sentiment). Though Industrialists were split up between both parties at the time (depending on whether or not they benefitted from tariffs mostly, though there were some Industrialists who voted Democratic out of laissez faire principle), Democrats got large majorities of the Fenian vote by tactics such as "twisting the lion's tail" by occasionally attacking the imperialism of various Republicans and comparing them to Great Britain, a surefire vote winner among the growing immigrant populations in northern cities. THough, there were candidates like Henry George, who ran for Mayor of New York City in 1886 as an Independent Democrat, who gained large working class support due to a wide alliance with the Land League, several Irish unions, and even some of the Priesthood in the city running off of a land tax platform.
Irish American leftism was a lot more based out of an attack on the idea of "landed" interests than off of the specific philosophy of Karl Marx and others that the German American left subscribed to. The history of the landed largely Anglican elites in Ireland is fundamental to understanding the leftism of the the poor in the late 19th century. Many of the elites charged confiscatory rates for many of the tenant farmers and the like who worked and lived on the land. It was therefore easier for many Irish in America to make a direct link between land ownership and capitalist abuse than to the detailed critique of capital found in the works of Marx that goes further in analysis on the entirety of the social hegemony in place. A lot of left wing sympathy among the group was rooted mostly in a long history of being second class and impoverished and subjected to foreign rule. Naturally, they and other ethnic groups (especially the Polish) felt targeted by the "Americanism" of the Republican Party, which is how you get such a division among certain groups that leaned left. Meanwhile, many German Americans had settled further inland and were suspect to a great deal of "Plains Republicanism" that also had a deal of populist intrigue and was more removed from the class divisions that existed further east. Though, as issues like Prohibition popped up as a Republican issue from the 1870's-1890's, German Catholics had a brief period of flirtation with the Democratic Party. And then Bryan and other Dry Democrats became more prominent which allowed the GOP to get back a window of opportunity among the group. German Catholics briefly (again) returned to the Democratic fold off of the anti-imperialism of Bryan and the supposed "neutrality" promised by Wilson only to become strongly anti-Democratic after the Wilson campaign used the opportunity of World War I to begin an anti-German campaign throughout the nation that helped nativist and Prohibitionist forces lead a crusade against all things German American.
In 1920 the Democratic Party managed to piss off both the German and Irish votes in the North, leading to a certifiable landslide by any definition of the term. With the Irish Free State being established and the immediate Civil War that followed many Americans who had a strong investment in the movement felt a measure of disillusionment. This, along with the rapid economic ladder climbing of the 1940's and 1950's and feelings of Americanism instilled in the community from the experience of World War II, would weaken what was once a solid Irish labor wing that aligned strongly with the Democratic Party. Further developments, like the Red Scare, integration, busing, and abortion, would only further divide a demographic that were once considered unparalleled in their devotion to the Democratic cause.
The tl;dr version of this: They were Democrats.
