How can someone be of two nationalities during the First World War?

Question

In Greenmantle, by John Buchan, an American man, John S. Blenkiron, was on a secret mission in Turkey during the First World War. He blended in with some of his enemies there and was convincing them to recruit his friend, Richard, whom he was talking to now:-

I argued that unless I had a very clear part with a big bluff in it I wouldn’t get the confidences which I needed. We’ve got to be at the heart of the show, taking a real hand and not just looking on. So I settled I would be a big engineer—there was a time when there weren’t many bigger in the United States than John S. Blenkiron. I talked large about what might be done in Mesopotamia in the way of washing the British down the river. Well, that talk caught on. They knew of my reputation as an hydraulic expert, and they were tickled to death to rope me in. I told them I wanted a helper, and I told them about my friend Richard Hanau, as good a German as ever supped sauerkraut, who was coming through Russia and Rumania as a benevolent neutral; but when he got to Constantinople would drop his neutrality and double his benevolence. They got reports on you by wire from the States—I arranged that before I left London. So you’re going to be welcomed and taken to their bosoms just like John S. was. We’ve both got jobs we can hold down, and now you’re in these pretty clothes you’re the dead ringer of the brightest kind of American engineer ... But we can’t go back on our tracks.

How can he be a good German and American at the same time? Does it mean he was just of a German origin?

Answer 1

In America, many people see themselves as being American but also partly identified with another nationality or ethnicity which is where their family came from. Hence the terms like "Italian American", "Chinese American", "Iranian American", "Irish American", etc. This is at least partly due to the nature of the USA as a country full of nth-generation immigrants: with the exception of Native Americans (a small proportion of the modern population), every American is descended from people who came to America from somewhere else. In this case, what we're looking at is the concept of a German American.

Yes, it just means he's of German origin, but it also suggests that he may have retained some elements of German culture, and (in this context) may also suggest a predisposition to sympathise politically with Germany in the war. Note that, at the time this story is set, the USA is still neutral, and therefore it's not strange for someone to be American but support Germany - they're not (yet) on opposite sides in the war.

From before the passage you quoted (emphasis mine):

“Your name is Richard Hanau,” Blenkiron said, “born in Cleveland, Ohio, of German parentage on both sides. One of our brightest mining-engineers, and the apple of Guggenheim’s eye. [...]”

And from somewhat after the passage you quoted (emphasis mine):

“I have heard of you,” she said. “You are called Richard Hanau, the American. Why have you come to this land?”
“To have a share in the campaign,” I said. “I’m an engineer, and I thought I could help out with some business like Mesopotamia.”
“You are on Germany’s side?” she asked.
“Why, yes,” I replied. “We Americans are supposed to be nootrals, and that means we’re free to choose any side we fancy. I’m for the Kaiser.”

(Here, of course, "nootrals" is eye dialect for "neutrals".)

Answer 2

Rand al'Thor has a good analysis, particularly about mixed identities in America.

However, I would also point out that the passage you've quoted isn't really talking about his actual nationality or ethnic identity, but about his sympathies and appearances. To be "as good a German as ever supped sauerkraut" means he is culturally and politically aligned to Germany (regardless of his actual nationality or citizenship). In a context like this, I would not find it unnatural to apply that to a person, regardless of their citizenship or ethnic background. And in particular, the phrase "you're the dead ringer of the brightest kind of American engineer" means that he bears a strong resemblance to a particular kind of person.

Basically, these are both assertions that Richard "looks the part." They don't necessarily say anything at all about his actual nationality.