“Children born abroad have always been considered US citizens.”
That is entirely false.
A child of an American citizen as a general rule. A family might be caught up in the imprecision of state department regs. I know of a case where the unaccompanied wife of a GI had a child in Landstuhl hospital and it took a private bill to cut through the regs and get a passport for the child.
No it's not....children born of foreign service workers, ambassadors, their staff, military personnel, etc are indeed citizens. I have a nephew born in Oberamergau, Germany and he is natural born, not nationalized.