AFAIK, the US has never, and still doesn't, "recognize" dual citizenship. If I become a citizen of Chad without renouncing my US citizenship, it changes absolutely nothing about my relationship with the US. Our laws do not recognize dual citizenship, they ignore it.
To become a naturalized citizen, one must swear ""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."
However, there is no enforcement mechanism to ensure that other countries don't still consider them to be citizens. Nor, if you think about it, can there be. We have no way to force other countries to "disenroll" their citizens who are naturalized here.
FWIW, Washington and Madison were both citizens of France.
The State Department website recognizes the concept of dual citizenship in the US now...
A U.S. national may acquire foreign nationality by marriage, or a person naturalized as a U.S. national may not lose the nationality of the country of birth. U.S. law does not mention dual nationality or require a person to choose one nationality or another. Also, a person who is automatically granted another nationality does not risk losing U.S. nationality. However, a person who acquires a foreign nationality by applying for it may lose U.S. nationality. In order to lose U.S. nationality, the law requires that the person must apply for the foreign nationality voluntarily, by free choice, and with the intention to give up U.S. nationality.
In other words, native Americans are second class citizens because unlike Mexicans they MUST relinquish their birth nationality if they attain citizenship elsewhere.
The oath to become a US citizen contains language saying that you give allegiance ONLY to the United States. However, that is not binding and plenty of immigrants who take that oath violate it (including Peter Jennings).
The old Ask The Imam website had an “expert” say that muslims were permitted to take that oath so long as they didn’t actually side with the US over muslim nations should we go to war.