In the past that may have been true. At least in my experience most white people don't even know their country of origin, and if they do it's really not that big of a deal. Ethnic festivals and holidays mostly just continue on as tradition now. They aren't signs of seriously separate cultures. You can't tell whether someone is Irish by how they talk, by how they dress, who they hang around, etc. The fact they are Irish is not an important part of their identity at all. These separate white cultures have mostly melted together over time into just "American culture".