Image links to: “‘No Irish Need Apply’: A Myth of Victimization” by Richard Jensen in the Journal of Social History 36.2, 2002: 405-429.
Here’s an excerpt:
Did the Irish come to America in the face of intense hostility, symbolized by the omnipresent sign, “Help Wanted: No Irish Need Apply”? The hard evidence suggests that on the whole Irish immigrants as employees were welcomed by employers; their entry was never restricted; and no one proposed they be excluded like the Chinese, let alone sent back. Instead of firing Catholics to make way for Protestant workers, most employers did exactly the opposite. That is, the dominant culture actively moved to create new jobs specifically for the unskilled Irish workers.
All that to say, maybe the signs aren’t even true! Historians: myth-busting and myth-building since at least circa 2002.
On the other hand, there are things like this cartoon from Life Magazine (11 May 1893):
Image likes to “Negative Stereotypes of the Irish” by Gwen Sharp in The Society Pages, 6 October 2008. Well worth a read! (And has lots of cartoons.)
History: proving that things are complicated since five-ever.