I think I can see that the ability to view restricted categories disappears when a user enters anonymous mode (see Anonymous posting -- but retaining original user permissions) but is there any similarity between the two users? What about trust level?
The trust level for anonymous users is locked at TL1, but I believe an admin can manually change this for specific anonymous accounts from the anon user’s admin page.
In summary, I think the anonymous/shadow user is a brand new TL1 user and does not inherit the actual user’s groups (hence preferences) or trust level.
It would be good if it could inherit these characteristics. But the way it’s structured, I can see that it would cause extra work (eg keeping group membership of multiple users in sync).