not a myth, although popularly touted as a myth by people to whom this fact is inconvenient. it's very easy to google examples of racism towards irish and italian immigrants.

https://www.google.com.au/search?q=irish+need+not+apply&sour...

here's where the "myth myth" started and was easily debunked by a high school student

http://www.irishcentral.com/roots/history/High-school-studen...