Drupal's cron job has no access to CiviCRM custom fields (Anon access to custom data?)
You need to turn on "Access all custom data" for anonymous users for a lot of very popular features (e.g. custom fields for anonymous users in profiles and webform_civicrm) to work.  Someone else can contradict me, but I'm reasonably certain this has no impact on security unless a) anonymous users also have access to contact records, or b) you have custom field sets whose access should be restricted via ACL.

I'm sure there's a way to allow access to custom fields to anonymous users via ACL, but that often strikes me as overkill.