The internal mechanics of OxWall are based on "events", that when an activity occurs ("see a profile", "upload a photo", "comment on X", etc) an "event" is generated with the information of the event .
A plugin can access these events and do something with those that interest you, such as preventing viewing a profile, for example.
There is no event that is generated when a specific field of the profile is displayed. Modifying the OxWall core would be possible, but it would be too many events and it would hurt the speed a lot.
It would only be possible by modifying the page "see a profile" by unfolding it in two and showing the complete or the simplified according to the roles. This involves modifying the OxWall kernel and also a plugin where you can assign which fields are displayed or not in the simplified view.