According to the chief medical officer for the American Lung Association, the only legitimate medical exemption is people who are on supplemental oxygen. Even patients with chronic lung disease can wear a non-N95 mask with no detrimental effects.

The CDC does recognize intellectual and developmental disabilities as legitimate medical exemptions, which I believe is the most common case we are seeing the US.

No, It has been determined time and time again that if you have a respiratory illness that means you're struggling to breathe so much that you can't breathe with a mask on, that puts you in the extremely high risk category from covid

The only legitimate reasons are associated with anxiety issues, which aren't medically exempt.