What is the manage_privacy_options permission in WordPress?
The manage_privacy_option permission was introduced in WordPress 4.9.6 as part of the new GDPR Privacy features.
Unfortunately, it doesn't yet work as designed. The permission is designed to control access to the Settings > Privacy page. Unfortunately, anyone with the manage_options permission can access this page and manage_privacy_options doesn't have any effect.
There is a ticket on WordPress.org to fix the behavior of this and related permissions. We'll update this when the problem is solved.