Is ethnicity still important to white ethnic groups in the 21st century?

Ethnicity is something that usually associates people with a different country and culture, and for Americans who have lived here for a long period of time I feel as if they associate with being "white" rather than any other ethnicity. In Jacobson's Whiteness of a Different Color, it says that being white in 1790 referred to anyone that is not black, which is an interesting concept because today it can be difficult to determine even that much because there is so much diversity within one single person.  It's important to realize that "whiteness" is socially constructed and not something that is genetically given to us.  Whether or not ethnicity is important to white ethnic groups is up to the opinion of every individual. That being said I still believe people associate with their ethnic groups, just not as strongly as maybe we used to. For example, I know that I am mostly from Irish and German descent, and I have an urge to go to Ireland to see where my family came from. I feel like this is more prominent in first and second generation citizens as they still have strong roots from where they originally, so as the generations continue they are more prone to associate with being white rather than being Irish for example.  I see it as kind of getting blended in with the American Melting Pot, so people would rather blend in and be seen as white then differentiate themselves in chances of being outcast.