Your medical record is private, but if a job has a requirement they can ask for proof of vaccine. It is up to you to provide it, and it is up to them to how to interpret it if you don't provide and how to handle it.
For example even before the pandemic it was a job requirement of you were in a medical field.
That's fine but I didn't have to show my vaccination record to my current employer. I literally sit at home and stare at a computer screen all day. That's different than a nurse at a hospital.
My sister works at Pfizer in clinical trials, her last day is next week. She literally had to submit negative test results every week since around May. She works remotely, doesn't live in the same state as Pfizer headquarters and sits in front of a computer all day. Tell me how that makes sense?
Your medical record is private, but if a job has a requirement they can ask for proof of vaccine. It is up to you to provide it, and it is up to them to how to interpret it if you don't provide and how to handle it.
For example even before the pandemic it was a job requirement of you were in a medical field.