When the Italians and the Irish and the Slavs and the Polish etc. Their livelihoods were here, but their hearts were in the old country. In short, the great, great grandchildren of those first generation immigrants love their ethnic origin, they value their ethnic origin, they are proud of their ethnic origin, but they are heir to many ethnic heritages, and do not see themselves as Irish or Italians first. They see themselves as American first - but they are still Catholics, or Protestants, or Jews. In other words, all that remains in these great, great grandchildren, of what the first generation prized, as a central part of their lives, is their religion.
Ethnicity is there, but peripheral.
Look at our experience in even so ethno-centric a society as India. Only in our religion are we the same, mostly. I think three or four generations from now, our great, great grandchildren may think with affection and sentiment and pride about their ethnic origins,but they will be Americans. Of course the trads think their ways will preserve our religion. And we think our ways will do a better job of preserving it.