Screw them, it’s none of their business.
Probably they will just stomp their foot and say we can require whatever we require to work here. It would take a judge or jury that will understand the principle involved in breaking HIPPA secrecy and practicing medicine without a license.
I remember when HIV was a big thing and the Health Dept tests were waved to keep the patients secrecy. They would rather have an HIV patient bleeding in you salad or spitting on your food just to keep his/her condition secret. It's really no different than an AIDS patient working at a machine shop that cuts himself on a tool everybody uses. The powers that be decided his secrecy was more important than everybody else's health. Today in Texas nobody takes the Health Dept blood test for STD's, Hepatitis, and Tuberculosis. This is especially dangerous with open borders and illegals bringing you food and cleaning dishes and tables.