If you need to disable “Sync” option for the Document Libraries in a SharePoint Online site, just follow the steps bellow:
- In the Site settings page, under the “Search” section click the “Search and offline availability” link.
- In the “Search and offline availability” page just change the “Allow items from this site to be downloaded to offline clients?” setting from “Yes” to “No” and press “OK”.
Navigate to any of the Document Libraries in the site and verify the “Sync” option is disabled.
Of course, this option to disable “Sync” is also available for OneDrive for Business site.