The custom profile fields can be disabled with the authentication plugins. This means that students can see the content but not edit it. This is the case for all of the custom profile fields besides the text area fields.

Theme boost and theme clean show (don't show) slightly different information.

Theme boost will show the label for the text area field.

Theme clean will not show the label or the text area field.

1. Probably the easiest way to reproduce is to create an external db for authentication. Add a field to be used for the custom profile text area field.
2. Create a custom profile field that is a text area.
3. Enable the external db authentication plugin (Site administration  ► Plugins  ► Authentication  ► Manage authentication).
4. Set the custom profile text area field to match with the external db and set "Lock value(xxxx)" to locked.
5. Log in as a student and go to the edit profile page (as a user from the external database).
6. Observe that either the field is not there (clean) or just the label is shown (boost).

My expectation is that the information would be shown with no option to edit it.