Anonymous, not logged in readers
By default, anonymous users (i.e., anyone not signed in) have read access to all public blog content and can subscribe to receive email alerts when new blog posts are made.
To prevent anonymous readers from subscribing via email:
Navigate to Control Panel Dashboard > System Administration > Blog Administration > Configuration > Default Settings.
Change Enable Email Subscriptions to No.
Click Save. The page is refreshed and shows a confirmation message. The link to subscribe to email alerts is no longer visible to anonymous users.