And that is exactly why the Constitution, our founding document, as well as the original SC opinions of the 14th Amendment, neither allows for dual citizenship. The founding fathers as well as the following generations, all the way through the civil war, rejected the concept of dual citizenship. But alas, we got it via fiat law thanks to a corrupt Supreme Court decision in the 1890's who used British feudal law rather than adhering to American law the same court had just upheld less than 10 yrs prior to the fateful decision and by the same SC Justice no less who's bank account profited greatly from the unconstitutional decision he made.
For practical purposes, dual citizenship only becomes an issue when one of two things happens: (1) the person tries to conduct themselves as a citizen of both countries (traveling with multiple passports, voting in both countries, serving in the armed forces of both countries, etc.); and (2) the person gets involved in a legal process where his or her citizenship is an important legal consideration.