This goes back much further than the 1920s. White America was quite racist up until the civil rights battles of the 1960s (and this racism continues to this day). The sole dissenting voice against the Civil Rights Cases and Plessy v. Ferguson, John Marshall Harlan, wrote in his dissent of Plessy v. Ferguson that
In view of the constitution, in the eye of the law, there is in this country no superior, dominant, ruling class of citizens. There is no caste here. Our constitution is color-blind, and neither knows nor tolerates classes among citizens. In respect of civil rights, all citizens are equal before the law.
While that sounds lofty, he also wrote in the same dissent that
There is a race so different from our own that we do not permit those belonging to it to become citizens of the United States. Persons belonging to it are, with few exceptions, absolutely excluded from our country. I allude to the Chinese race.
He wrote this in part because the Chinese Exclusion Act of 1882 had already been law for fourteen years at the time of the Plessy v. Ferguson decision. Harlon used that law and the strong anti-Asian sentiments of the time to illustrate how very bad a precedent the majority was creating in that ruling. However, even Harlan (who was very nondiscriminatory by the standards of his time) could not get over anti-Asian sentiments. He ruled against people of Chinese descent a number of times.
Anti-Asian sentiments continued in America well past World War II. A large number of Korean citizens migrated to the US after the Korean war, and a large number of Vietnamese citizens migrated to the US after the Vietnam war. A large number of those Vietnamese migrated to areas that had conditions similar to home: Hot, humid, and close to water so they could fish. That would be the very, very deep south. Some rather nasty racist incidents arose as a result of that migration.
The above does not directly address the anti-Japanese sentiments expressed in the photo shown in the question. My answer addresses anti-Chinese, anti-Korean, and anti-Vietnamese sentiments. It does not address anti-Thai or anti-Japanese sentiments in the US. And yes, those sentiments did (and still do) exist. Witness the Japanese internment camps during WWII. "They don't look like us" goes back to before humans knew how to write.