The majority of people who do not wear masks do not wear them because they don't believe in Covid or mask-wearing - not because they genuinely cannot wear a mask.
The thing is if you are TRULY exempt, it's not as if you are exempt due to a dreadfully embarrassing very personal health condition.
It's either going to be a breathing condition (which IMO you shouldn't be out anyway with a lung/breathing condition severe enough to prevent you breathing through a mask) or due to an anxiety or a learning difficulty/autism diagnosis or similar?
It's not as if they're asking you to show them a boil on your bottom when you're asked why you are exempt so I don't see the big deal?
The way I see it, you can't be exempt from wearing a seat belt in a car, or showing a blue badge when parking in a disabled space, or from wearing a hard hat/boots/safety glasses in certain jobs whatever your condition.
But for the small minority who truly, genuinely cannot wear a mask surely you would be happy to provide some proof - be that a letter showing your diagnosis, or your medication (eg inhaler) or similar.
I am asthmatic and wear a mask. If I genuinely couldn't I personally wouldn't go out at all, but if I did, I would be happy to show my inhaler as my reason for not wearing a mask.
I don't understand why others can't do the same.