The inspector badge on the left is a prewar issue, probably dating around the early 1930s.
The badge on the right is a rare circa 1900 California State Board of Health inspector badge with a painted red cross at its center. The badge was manufactured by Moise-K of San Francisco, California, and is maker-marked on the reverse side. This badge was worn by an inspector during the bubonic plague outbreak of 1900–1904 that was centered on San Francisco’s Chinatown. It was the first plague epidemic in the continental U.S.
According to Wikipedia, the epidemic was recognized by medical authorities in March 1900, but its existence was denied for more than two years by California Governor Henry Gage. His denial was based on business reasons, to protect the reputations of San Francisco and California, and to prevent the loss of revenue due to quarantine. The failure to act quickly may have allowed the disease to establish itself among local animal populations. Federal authorities worked to prove that there was a major health problem and they isolated the affected area. This work undermined the credibility of Gage and he lost the governorship in the 1902 elections. George Pardee, the newly elected governor, implemented a medical solution and the epidemic was stopped in 1904. There were 121 cases identified, including 119 deaths.