End users have the ability to follow/unfollow Organization Requests in the Help Center.

https://support.zendesk.com/hc/en-us/articles/115002997048-Submitting-and-tracking-requests-in-the-Help-Center-customer-portal-Guide-Professional-and-Enterprise-#topic_vgd_mqd_yy

There isn't a way for a Zendesk admin to toggle this for one or all users under an organization. It would be helpful if there was a way to do this in the Zendesk admin interface as well as API. 

Reference internal ticket: 6266570 and 6271752