I'm a nurse specialising in Occupational Health. (I assume you know what we do? Genuine question...many don't understand our role!
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Obviously it would depend on the outcome of an OH assessment and discussion around history, treatment and symptoms but this would definitely be a reasonable adjustment we would recommend to their line manager. (Ask that they are exempt from certain tasks).
This may be temporary until optimal treatment or permanent if they've been assessed several times and treatment hasn't particularly improved their ability to do this one particular thing. Especially if it is a small part of their role.
If the thought of doing this is likely to worsen their overall symptoms and contribute to a deterioration in their health then it may also lead to a sickness absence.
Some may argue that a person with symptoms which affects their ability to do their full role should actually be off sick. But for many it is actually better for their MH to remain in work and in a routine, feeling that they're contributing etc etc. Lots to think about.
It is likely to be an agreed adjustment. Your/their line manager will not be allowed to discuss or confirm this due to confidentiality though.
There are many many people who are considered as being protected by the Equality Act 2010 for all types of health conditions and symptoms.
Please just bear in mind that them being aware of your thoughts on this may very well further impact upon their anxiety/MH.
I do see above that PP have also offered advice which has given you food for thought, so that's great
I'm sure in an ideal world they would love to live without anxiety.