Fatal error in CiviCRM 4.7.7 on Drupal 7

After upgrading from 4.7.6 to 4.7.7 on Drupal 7.43 I get the following fatal error

CRM_Core_Exception: Invalid Entity Filter in CRM_Core_BAO_CustomGroup::validateSubTypeByEntity() (line 658 of [...]/public_html/sites/all/modules/civicrm/CRM/Core/BAO/CustomGroup.php).

I followed the official upgrade process step by step, including replacing all files and clearing templates_c. The upgrade initially appears to succeed - the error happens after a screen refresh and then persists, making the whole site unusable. I've tried disabling all CiviCRM components and extensions, and all Drupal modules that use CiviCRM, as well as clearing all caches.

The error can be cleared by removing /sites/all/modules/civicrm and functionality can be restored by reinstalling the previous version of civicrm (4.7.6) to that folder.