Are you seriously in the field of medicine? This is not even in the same ballpark of discussion. If someone is HIV or Hep C positive, they should absolutely disclose that to anyone they could potentially infect before they engage in sexual activities/needle sharing etc. That's just basic common decency for a fellow human. It's also the law in several states. I am sure you would be plenty upset if one of your patients was HIV+ and purposely lied to you about their status after you got a needle stick or eye splash while caring for them.
The HIPPA/personal health info arguments amuse me too. People can voluntarily allow anyone to have access to their healthcare information. If you allow the surgeon to talk with your wife about how the procedure went, it doesn't violate HIPPA. Showing your vaccine passport to avoid an unnecessary COVID test or quarantine with travel would be exactly that. Voluntary disclosure.
People have the right to skip the vaccine. Businesses have the right to afford privileges to people who choose to become vaccinated and voluntarily disclose that information for said benefits. The Miami Heat just want to generate ticket sales. If a vaccine allows them to put 200 people in a section vs 30, go for it. If you don't want the vaccine or don't want your medical information disclosed, go sit in section 220 instead. Your body, your choice. Their arena, their choice. Now, if they do decide to allow a group sex event in the American Airlines Arena, they should probably ask for the HIV ID that you propose.