For older versions of Confluence, the users could perform this modification through a customisation according to this KB article, but, this does not apply for the latest versions.

This is a feature request to provide the ability for the system administrator to disable the profile editing for the users with non-admin permissions. It would be awesome if either the options in the left side of the profile were removed, once this is checked or if a warning gets displayed like: "Profile editing is not enabled in Confluence. For any modifications needed, please, contact the system administrator"