My response was essentially, "I can do it, but we will need to explain why we are going against CDC guidelines or else I see a mass problem on our hands. Can you get that reasoning for me so I can share it?"
A few hours later, the request for the memo was rescinded. Big win in my book.
The problem is when employers make everyone wear a mask UNLESS they prove they aren't vaccinated. So they aren't exactly forcing you to give your health information to them...but there is HUGH incentive and pressure to do it or get the injection.