No they don't. They can hold dual citizenship and two passports. We recognize that other countries can confer citizenship. As long as the naturalized citizen is not applying for other citizenship from another country. I thought the information I provided to you was quite clear. We recognize dual nationalities.
Dual citizenship had previously been banned in the United States, but in 1967 the US Supreme Court struck down most laws forbidding dual citizenship.
However, the US government remained disdainful of dual citizenship for some time. To this day, candidates for US citizenship through naturalization are forced to (at least hypothetically) renounce their previous citizenship at the United States naturalization ceremony.
The renouncing of one’s previous citizenship is part of the oath that new US citizens must take, and failing to honor that oath could result in the loss of citizenship in the United States.
Some cases that have been brought before the Department of State in the past involve people who became naturalized US citizens but maintained a residency and life in their country of previous citizenship.
While most countries recognize the Oath of Allegiance in the United States to be a binding contract regarding one’s citizenship, other countries have stated that the oath has no effect on their own citizenship laws. The US government used to aggressively pursue these cases to get the dual citizens to renounce their citizenship, but this is no longer the case.
Additionally, young children who naturalize in the United States along with their parents didn’t take the Oath of Allegiance — even though their parents did — and can technically still hold on to their previous citizenship.
People who have held dual citizenship since birth or childhood — or who became citizens of another country after becoming a US citizen and were not asked to renounce their previous citizenship — can remain dual citizens in the United States
That's the cite from Immigration and Naturalization for the current oath of allegiance taken at naturalization. Page 28.
"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."
It is from the US Code.
INA: ACT 337 - OATH OF RENUNCIATION AND ALLEGIANCE
Sec. 337. [8 U.S.C. 1448]
(a) A person who has applied for naturalization shall, in order to be and before being admitted to citizenship, take in a public ceremony before the Attorney General or a court with jurisdiction under section 310(b) an oath
(1) to support the Constitution of the United States;
(2) to renounce and abjure absolutely and entirely all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty of whom or which the applicant was before a subject or citizen;