How to filter a view based on tags applied to
So, shortly after posting this question I worked out how to do it.

When I built this site I included the facility to create a Views relationship that points at the "referred to" user (the "patient" in the above example). So, I created this relationship in the view that I built. I then created another relationship that was itself based on the first relationship but pointing at the node created by the Content Profile module.

Then, I created a filter based on the second relationship, that filtered based on the taxonomy term I'd created (i.e., the "diabetic", "pregnant" stuff above). That did the trick.