What did immigrants from Europe like Ireland, Germany, etc think of the practice of slavery in the United States when they first arrived? Were they shocked? Disgusted? Was it not that big of a deal to them since various countries in Europe were practicing slavery is their own colonies?
I'm no historian, but I do know that for the most part immigrants were apathetic to the Civil War, with the exception of some Irish.
There are many accounts of northern immigrants being heavily anti-Civil War because they were the ones being drafted into the military. General Grant's reputation of being a "butcher commander" who would use his troops as pawns and have them slaughtered in hundreds was well alive, and there was great resentment by many immigrants who came off the boat and were handed a rifle and told to go down south and fight for the freedom of lowly blacks in the place of the white people who were throwing rocks at them and discriminating against them.
A particularly famous case is the New York City Draft Riots in 1863 where the city burned, rioted, protested and looted for four days.
I think it is difficult to narrow down exactly how they felt about slavery because that comes down to how racist each individual was. But they were definitely against the Civil War because the south being part of the union didn't affect them. For example, famous general and populist irishman George McClellan ran on the Democratic ticket of ending the violence of the Civil War and allowing slavery. McClellan carried the immigrant heavy New Jersey, as well as New York City and Boston.
On the flip side, there were many immigrants, Irish in particular, who empathized with the blacks in the south and had great pride in their adopted homeland. They loathed the British who had occupied Ireland for hundreds of years and starved the Irish into diaspora. They felt that they had been slaves working to feed the British populace and saw parallels with the American South.
What's more, the south's appealing to the British to side with them in the Civil War gave the Irish further cause to hate the South. And, furthermore, these same prideful Irish saw America as a place where immigrants could rise to the top and be free. You may have heard of the famous Fightin 69th of New York who fought at Bull Run? One of the reasons they are famous is because Michael Corcoran was an Irish-American Union General who defied the Federal Army's order to march in parade welcoming the Prince of Wales to New York City for a state visit.
You have to keep in mind that the vast majority of the non English immigrants during the Civil War and leading up to it came from Ireland, Germany, Poland and Scandinavia (however these Scandinavians settled in the rural northwest where they were kind of away from all the happenings back East) and there was great turmoil in all of these countries at the time, so without doubt their lives were bad enough that they weren't worried about the innate liberty of blacks.
Some great things to check out if you are interested in this strain of history is
Gangs of New York, a 4 star immigrant movie starring Leonardo di Caprio, Cameron Diaz, Daniel Day Lewis and John C. Reilly, directed by Martin Scorsese
Music by The Wolftones, an Irish folk-rock band that sings about the tumultuous history of Ireland before and during the Revolution