I did a very rudimentary google search and see that the federal government requires a bunch of vaccines including influenza and Covid-19[1] for obtaining a visa. The CDC publishes a "menu" of state hospital vaccination laws[2]. Those sound like they both clearly fit "many contexts in the US that required a flu vaccine" the parent mentioned.

[1] https://www.uscis.gov/tools/designated-civil-surgeons/vaccin...

[2] https://www.cdc.gov/phlp/docs/menu-shfluvacclaws.pdf