Your loyalty should lie with the United States, not the nation of your ancestors. This sort of ancestral-country-patriotism is not good. Let me quote Theodore Roosevelt:
"There is no room in this country for hyphenated Americanism. When I refer to hyphenated Americans, I do not refer to naturalized Americans. Some of the very best Americans I have ever known were naturalized Americans, Americans born abroad. But a hyphenated American is not an American at all … The one absolutely certain way of bringing this nation to ruin, of preventing all possibility of its continuing to be a nation at all, would be to permit it to become a tangle of squabbling nationalities, an intricate knot of German-Americans, Irish-Americans, English-Americans, French-Americans, Scandinavian-Americans or Italian-Americans, each preserving its separate nationality, each at heart feeling more sympathy with Europeans of that nationality, than with the other citizens of the American Republic … There is no such thing as a hyphenated American who is a good American. The only man who is a good American is the man who is an American and nothing else." Source: https://en.wikipedia.org/wiki/Hyphenated_American
I'm sure these hyphenations exist in every part of the World. It's these hyphenations that make a Nation stronger IMHO. In India, we have Luso-Indians (or Portuguese Indians), Dano-Norwegian Indians, German-Indians, French-Indians, Chinese-Indians, Parsis (Persian-Indians) etc. who made India their home. We don't force them to call themselves only "Indian". Why would you want someone to sever their past and their rich cultural heritage just to prove their Patriotism? Isn't that against the very notion of a "Free country" / "Republic"? As long as the citizen is not involved in any anti-National activities (terrorism, hate speech, espionage, disdain/disrespect for the Country's laws etc.) there is no need to bring that citizen's loyalty under suspicion.
There is no measure with which one can "feel more sympathy" for their ancestral-country than the country for which they have accepted citizenship. "Feel more sympathy" for what? Would an adopted child "feel more sympathy" for it's biological parents than the parents that nurtured it?
No reason why not -- those words were written the last time the US was having a huge backlash against immigrants. In that case it was a backlash against Catholics, and Europeans who weren't as white as Northern Europeans.
Today, being a hyphenated American is no big deal.
"There is no room in this country for hyphenated Americanism. When I refer to hyphenated Americans, I do not refer to naturalized Americans. Some of the very best Americans I have ever known were naturalized Americans, Americans born abroad. But a hyphenated American is not an American at all … The one absolutely certain way of bringing this nation to ruin, of preventing all possibility of its continuing to be a nation at all, would be to permit it to become a tangle of squabbling nationalities, an intricate knot of German-Americans, Irish-Americans, English-Americans, French-Americans, Scandinavian-Americans or Italian-Americans, each preserving its separate nationality, each at heart feeling more sympathy with Europeans of that nationality, than with the other citizens of the American Republic … There is no such thing as a hyphenated American who is a good American. The only man who is a good American is the man who is an American and nothing else." Source: https://en.wikipedia.org/wiki/Hyphenated_American