In the post war period the gates were opened to Eastern European Catholic farmers ~ Ukrainians, Russians, Poles, more Germans, etc. The railroads made it possible to convert the vast American desert into a world of wheat and other grains. Coal mining brought in even more of them.
Once all the plants were planted, fields ploughed and barns built, the Italians and Greeks, all Catholic, came into the Eastern cities ~ and California ~ to build urban infrastructure.
When you speak of the Protestant "Irish," you must be referring to the Scots-Irish. The Irish of the Northern states, particularly the Northeast, like the Kennedy clan, are immigrants from Ireland, and are, of course, Catholic.
The Scots-Irish from Ulster, or Northern Ireland, a very different story. Protestants to the man, making up a large part of the south, Bible belt Protestants.
the Italians and Greeks, all Catholic
Wouldn't the the Greeks be Greek Orthodox?