That’s true. I doubt too many Americans would send their sons to fight for the Jews. While not as segregated as the blacks, I believe there were a number of hotels and restaurants that would not serve Jews, if they were known as such.
On the other hand, not so many Americans would have fought for the Armenians in World War 1, or the Ukrainians in the Holodomor, or for the Chinese, or the Ethiopians, or Sudanese Christians today....
It was controversial in its day. The plot is a gentile writer agrees to go "under cover," pretending to be Jewish to see first hand the subtle and not so subtle discrimination he would experience.
Darryl Zanuck got the idea of making a film based on the novel when he was denied membership in the Los Angeles Country Club because people wrongly thought he was Jewish.