I had a childhood friend who was born in Germany while his dad was in the Air Force and he was told he was not eligible to be President. They used to advise military wives to go home for the birth of their children if they wanted to preserve natural born status.
Civics classes taught born here of citizen parents, no divided loyalties, no foreign citizenships, solely a US citizen.
Are there differences between the Navy and other services since a US ship is always considered part of the US just like land within any state is ?
We were in Germany living on an American kasern (which was considered American territory) when our second daughter arrived, in an American military hospital. Nonetheless, three years later, upon our return states, we went into the big city to the immigration office to confirm her citizenship. When the nice lady asked our daughter to hold up her hand and give her name, she proudly replied “Mary Jane Smith d’America.” :-)