How to make the callback URL from Mailchimp accessible from anonymous users in Wordpress?
WordPress does not require that a role be given to users who only visit your site (e.g. to read posts) so long as it is public - roles are only required when logging in. However, for a WordPress client using the MailChimp sync, we found that we needed to create an Anonymous User role with the webhook permissions assigned - once you do this, pasting the webhook in MailChimp should no longer result in an error. 

To clarify, no one has to be assigned the Anonymous User role for this to work.

Hope this helps!
Tamar