Not to diminish the severity of it, but surely reconciliation on a national scale was helped by the fact that both sides could honestly claim that they fought to do what they believed was best for Ireland? Though I imagine that the wounds between families who fought on opposite sides run deep still, especially with people alive now who witnessed the war firsthand.
By comparison, our war had no such salve. The South, right or wrong, wanted out entirely, not just to change the government. Relationships between the sides were better in the past though, especially shortly before your Civil War started. In 1913, tens of thousands of Confederate and Union veterans met to commemorate one of the key battles. Later on, Confederate veterans were treated the same as Union veterans by Congress.
Nowadays, such courtesies would not be given to “evil, slaveholding racists”. Instead, people of a certain political persuasion use the memory of the war as a bludgeon to push for policies that they want. I remember one columnist who argued that gun owners should pay extra taxes and that those extra taxes should be higher if you happened to be white and live in a Southern state because of the Civil War.