In the USA, Irish culture is an individual accomplishment which is acquired, usually as a result of an investment of time and money. It has no necessary relationship to one's ancestry. The Irish-culture-in-a-can that we enjoy here includes Irish music that (I suspect) my Irish ancestors wouldn't have been caught dead listening to, Irish dances that my Irish ancestors wouldn't have been caught dead dancing, and Irish clothes that my Irish ancestors wouldn't have been caught dead wearing. Their emigration here has had the effect of freeing me from their Irish prejudices, thereby allowing me to appreciate some genres of Irish music and dance as I suspect they would not have.