In what sense did the 1930s witness “an acceleration of cultural assimilation”?

The 1930s were a period of cultural assimilation in the United States as more of its immigrants were either American citizens or were in the process of applying for citizenship. Also, more of these immigrants adopted "Americanized" spellings of their last names and spoke English than ever before. This was due to a few factors.
During World War I American leadership spoke out against what it called the "hyphenated American" and demanded his full loyalty. This was important as the United States was afraid of sabotage efforts funded by the Central Powers. This hatred of hyphenated Americans persisted after the war as Americans feared a Communist takeover and anarchist plots. The United States also passed stringent immigration quotas designed to affect those from Eastern and Southern Europe—these new immigrants were likely to settle in enclaves with their kinsmen in major cities and adopt English slowly. By adopting English, many new immigrants hoped to "blend in" with mainstream America and be hired for jobs. By the 1930s there was a sharp reduction in foreign-language newspapers as most Americans, whether longtime residents or newly arrived, learned and used English.