This might be more well-suited to /r/asksocialscience, but I find it interesting that the social ascension of Italian, Jewish, Polish, Armenian, and Irish Americans into the "white mainstream" appears to coincide with the Second World War.
Millions of white Americans from disparate regions and ethnic backgrounds served together in the same unit, and wartime media often exhibited diversity among Americans. In addition, the United States battled two foes who were explicit ethnic nationalists.
Did this integration of New York Italians, Georgia Scots-Irish, and Wisconsin Germans play any role in bringing marginalized European Americans into the fold?
It's often hard to ascribe causal force for single events on long, unfolding processes. It likely had some effect, but the idea was already long in place. The term "the melting pot" in reference to American identity, after all, comes from a 1908 play.
Will Herberg's very influential 1954 Protestant, Catholic, Jew argued that, since the 1920's at least, American had become a "triple melting pot", where ethnic (and within Judaism and Protestantism, sectarian) identities began to matter less and the general religious affiliation matter more. Especially during the Cold War, they were just three different but acceptable ways of being American.
This very interesting contemporary reflection on Herberg's book and its argument. The author notes that Herberg didn't coin the term "triple melting pot":
He borrowed the phrase from Ruby Jo Kennedy, a sociologist who published in 1944 an article on intermarriage in New Haven called “Single or Triple Melting Pot?” Kennedy had examined 9,044 marriages from several different years (1870, 1900, 1930, and 1940) to chart the decline of endogamy among people of the same nationality (Irish, Italian, Polish, etc.) and the rise of endogamy among the three religious groups. By 1940, Kennedy found that, in New Haven at least, Catholics married Catholics 85 percent of the time. Protestants married Protestants nearly 80 percent of the time. And Jews married Jews 94 percent of the time. “Culture [i.e. ethnic] lines may fade,” she concluded from her study, “but religious barriers are holding fast.”
Which is to say, the closing of ethnic division and the emergence of religious divisions was something underway long before the War. And as the author linked above points out (he's a historian, and author of Tri-Faith America: How Postwar Catholics and Jews Held America to its Protestant Promise), the importance of religious divisions seems similarly fleeting and that by 1967, the Kerner Commission reported that:
the Kerner Commission, declared that America was “moving toward two societies, one black, one white--separate and unequal.”
But in all these narratives, the anti-Communist Cold War is emphasized more than the experience of fighting in WW2, and it's important to remember that the post-War relative White racial unity was something that was built over the preceding half-century.
How much was it WW2 and how much was it the economic prosperity that the US enjoyed following the end of the war ?