All very good points.
But because the genetics of the Irish in America allowed their culture to change so dramatically in such a short time does not necessarily mean the same is true of all other ethnies.
IOW, that the negative Irish traits you mention were cultural rather than genetic in origin does not mean other ethnic groups with similar negative behavior may not have those behaviors be more genetic in origin.
Certainly could be, and I hope that is the case, but that the Irish can change does not of itself prove that any other group can.
IOW, that the negative Irish traits you mention were cultural rather than genetic in origin does not mean other ethnic groups with similar negative behavior may not have those behaviors be more genetic in origin
Nobody doubts that some differences among groups of people is due entirely to culture, relgion, or socio-economics. For example, the violent and barbaric behavior we associate with Arabs is mostly due to the current interpretations of Islam that are prevalent. Christian Arabs are often prosperous businessmen while their Islamist brethren live in slums. Similarly, England and Holland were in many ways economically and technologically more advanced than Germany (or rather, parts of the Europe that have since been unified into Germany) in the 16th-18th centuries, because trade exposed them to goods and ideas of the outside world at an earlier date. Obviously genetics has nothing to do with that, just as it has nothing to do with your examples of the socio-economic status of Irish-Americans between the late 19th century and today.
However, because culture and socio-economics account for some differences, you can't jump from that to making the claim that it explains all differences. When a group of people makes a very quick leap from under-achievement to achievement (Irish Americans) or vice-versa (Arabs), you can't blame or credit genetics. However, what of groups of people who have throughout their history been underachievers (or have been high-end achievers throughout their history)? Until Europeans arrived, no Sub-Saharan African country ever had a 2-story building. Similarly, east Asians seem to have no trouble adopting the technology and science of the west, yet in spite of being exposed to them in more or less the same way (Colonialism and trade), Africans never assimilated these things. While this doesn't in itself "prove" that genetics is to blame, it does strongly suggest that there's something else involved besides culture and good luck/bad luck.