If you are maskless never wear an exempt lanyard or badge, that's almost as bad as wearing a mask, it's a mark of who's complying with the government, it says 'I agree with the government', it also marks you out for 'special attention'.
If you are challenged by security or shop staff, just say 'I'm exempt', do not qualify it with anything like 'I have xxxxxxx' or 'I suffer from xxxxxx' it's not your obligation to disclose any qualifying evidence of your exemption and the government have said you should not be challenged.
It is against the Equality act 2010 to demand evidence of your exemption.
If the person persists, tell them it's against the Equality act 2010, and they are personally liable to a fine of up to £5000, stress the personally and the £5000, that should shut them up.
If they discriminate against you, tell them they are personally liable of a fine from £900 to £9000 under the Equality act 2010, again stress the personally and £9000
Or just show them this....
Here is the whole pdf document...
All the best, clownworld