The root cause of this issue is due to insufficient permissions for the user. To grant permission of customizing the "Selected Defect Fields" in “Automail” configuration page, the "Customize Project Entities" permission is required, because this is to customize the defect entity. As per the design, the granularity of control over the permission is on customizing all project entities, so there is no option to allow customizing defect entity only.
If the group users only need to customize the automail condition (the "To" section), then "Customize Project Entities" permission is not required.
If a group user has the permission "Set Up Groups", then the "Customize Project Entities" permission is not required, as "Set Up Groups" permission is a root permission.