Private Blog and MailChimp RSS Campaigns

I love the plugin, but need a workaround. I’m trying to set up MailChimp so that I can send out email notifications whenever something new is posted, but I need access to the RSS feed to do this. But I don’t want to make the feed public. MailChimp has this page that says I can access the feed with a username and password, but the private blog plugin only sets the password. If there is a hidden username somewhere I don’t know what it is.

https://www.ads-software.com/extend/plugins/password-protect-wordpress/