Some people take NewsFeeds for granted, and every so often you see an anxious query
Why can't my readers use a newsreader to read my blog, when I make the blog private?This is as if newsfeeds are just another content protocol.
The concept of private blogs, which require authentication, is relatively recent, compared to newsfeeds.
Both Atom and RSS protocols have been in use, well before dynamic templates and authenticated blog read access were provided, as Blogger features. This limitation affects both BlogLists, and email distribution of the blog feed, and Following.
None of those features are available for Private blogs, right now. Native Atom and RSS did not contain any provision for authentication of the reader.
Anybody who knows an Atom or RSS feed URL can subscribe to that feed, using any of several different procedures. Since access to a newsfeed can't be restricted, it would be meaningless for a newsfeed (with universal access) to be published for a private blog (with restricted read access).
When you change permissions on your blog, so only specific individuals can read it, the newsfeeds for the blog are closed. This may change in the near future. Recently, changes were put into Blogger to enable validation through an RSS V2.0 feed, which is hoped to eventually result in the ability to authenticate reader access through a newsfeed reader.
Search engine access to your blog is controlled separately, and you may need to check those settings too.
For right now, a solution using Google+ may be the best choice for publicising private blogs.