It's complex. My wife's father-in-law immigrated from Italy to escape the destruction wrought by fascism in WWII and seek economic opportunity. He was part of a diaspora of a small village in Abbruzze that settled around Binghamton, NY. I would say that they all love Italy and they all love the U.S.

Those are people I know very well because I have been to so many parties, dinners, and other events with them. I've seen the same thing with people from India, China, Sri Lanka, etc. I'd assume that it's the normal condition of immigrants.