But what does US law say as opposed to how we might think things ought to be?
"Section 349 of the Immigration and Nationality Act (8 U.S.C. 1481), as amended, states that U.S. citizens are subject to loss of citizenship if they perform certain specified acts voluntarily and with the intention to relinquish U.S. citizenship. Briefly stated, these acts include:
1. obtaining naturalization in a foreign state (Sec. 349 (a) (1) INA); 2. taking an oath, affirmation or other formal declaration to a foreign state or its political subdivisions (Sec. 349 (a) (2) INA);"
The acceptance of a Vanuatuan passport woluld be prima facie evidence for the relinquishment of US citizenship, in that you'd have to perform one of the other of these two conditions (most likely the second, as Vanuatu would already have naturalized you with your permission). The application for the Vanuatuan passport would show a positive intention to relinquish US citizenship.