I suggest you have the HR department handle the client inquiries.

Clients like that, you don't need. If that threatens your employment, then you don't need that job either.

I'd tell them it's none of their business and let the chips fall as they may.

Refer to Osha privacy laws

I would just say I’m not required to disclose my private medical information and I assure you we are taking all precautions to prevent the transmission of covid 19. Then just wear your mask. 😂

Your reply: “Jesus Christ is my Lord and Savior therefore I am fully covered!”