There was a time when people came to America to be Americans. They WANTED to be Americans and all that entailed. I was blessed to participate in helping with classes to help new immigrants from all populated continents (including ours) to assimilate into American culture, to learn the language, to learn the more critical basic laws, to learn the content and respect for the Constitution, to learn our Pledge of Allegiance and the symbolism in our flag, etc. And there were no more proud people in the world who stood up at their swearing in ceremony, who recited the Pledge of Allegiance, who took the oath:
(Working from memory)
"I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state or sovereignty, of whom or which I have heretofore been a subject or citizen; that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law; that I will perform noncombatant service in the armed forces of the United States when required by the law; that I will perform work of national importance under civilian direction when required by the law; and that I take this obligation freely without any mental reservation or purpose of evasion; so help me God."
(and then they sign a written oath containing the same language.)
When you see them reverently facing our flag, reciting the Pledge, many with tears of joy streaming down their cheeks, (and also my cheeks when I was in attendance), there is nothing else to describe it.
From then on they were Americans who happened to be born in another culture. They were not asked to renounce their culture and at times we all joyfully share in the festival traditions of the Chinese, the Irish, the Russians, the Italians, the Mexicans, et al. But they also assimilated into and enriched the unqiue American culture. .