During war or crisis, evacuation flights for emergency purposes usually organized by governments. However, those are intended for citizens of that country. For example, there were evacuation flights intended for French citizens stuck in the UAE during the initial stages of the Iran war following a drone attack, but what happens if the traveler has both a French & American passport? Which government takes charge on the situation?
Evacuation is straight forward when the person only has one nationality rather than two since that nation only ensures their safety & rescue while someone with two passports: let’s say both the US & France want this person out of the danger zone, but who takes the sole responsibility if both countries want the same thing? It can’t do both, has to be one or the other even if the French plane arrived first before the American one.
If the dual passport holder is lucid and able to make decisions, they can choose which country’s evacuation effort they will take advantage of. Neither country is in any position to deny this, even if having the other nationality is in violation of the law in the first one. Rescue first, prosecute later.
If the person is unable to make decisions for themselves, there are a number of situations that are possible. Maybe the first consular staff on the scene takes charge; nobody looks for a second passport of a person they don’t know when they located the first. If for whatever reason both consular outfits are involved, they figure out who will be in charge. Probably the one where the unconscious patient has spent the most time in living most recently. A lot of that will have to do with how well the countries get along.