Naturalization does require the following oath:
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; ...
In practice, this is taken to mean that in the case of any conflict in responsibilities between your US citizen and any other citizenship, the US responsibilities must be considered first.
No dual voters. All of this immigrant dual citizen crapola is less than 30 years old.