I was listening to the song 'No Irish Need Apply' and decided to look it up. There's newspaper ads that show that 'No Irish Need Apply' was a thing, but I keep seeing references to a paper by Richard Jensen (retired Professor of History, University of Illinois, Chicago) saying they didn't exist, and that all the evidence is anecdotal.

Did they, and to what extent were the Irish discriminated against in 1840's - 1930's America?