Skimming some stuff on late 19th century boxing, it seems that most of the big-name boxers in the US were Irish. Is there any particular reason for this? My first guess would that it's just a matter of the Irish diaspora being poor enough to consider being repeatedly punched in the face as a career path, and heavily-concentrated enough in the citities for that to actually pan out on occasion, but if that's the case, why don't we see more Italian, Jewish or Polish boxers?
If you look at a lot of the early 19th century boxers, after Molineaux, a good number of them are Irish, or Anglo-Irish. As Bombshoo said, Irish exposure to Boxing gave them a leg up on the competition as it were in the 19th century, and the only other population that enjoyed a similar advantage, the English, were pretty much gone as an immigrant community by the late 1800s.
Additionally, the Irish were kind-of-sort-of already integrated at this time, to a much better extent than the Italians, Poles or Jews were at the time. It tended to draw their attention to general American past-times rather then looking inward towards their own communities (which is why the Jews, Poles and Italians began to be so noticable later on in the history of American Boxing).
Lastly, settlement patterns did play a very significant role. While we tend to think of Boxing as an Urban phenomenon, anti-prize fighting laws were in place throughout the North East. While they certainly still happened in places like New York, it added an additional risk to large financial backing to boxing matches, which meant that most Boxing Matches
of significance in this time period happened in the American west, which never bothered to regulate Prize fighting since that was never really a thing among their native population.
The most common places for these fights were Texas, Nevada, California, and above all else New Orleans. New Orleans in particular was a city of immense Irish Immigration and while few of the Irish champions of that era came from these places, the superior degree of integration and already existing Irish populations in these regions certainly meant that young Irishmen would be more comfortable moving to these regions and more likely to move in the same social circles. African Americans similarly did very, very well in the late 19th century possibly because they enjoyed similar advantages over newer minorities.
EDIT: Oh, another contributing factor was the Irish tendency towards police service, which was instrumental to introducing Americans towards boxing and physical culture in general at the time.
