Recently I had issues with MU privacy plugin (host = wpengine). It seems that sometimes it just doesn't work: password protected, registred users.. making it public and vice-versa.
I had a long support thread with wpengine and the conclusion is that it should be related to a caching issue. Is it possible?
Here is their input:
Yes, the plugin is most likely not working because it is not compatible with caching. We do have an additional layer of caching that cannot be disabled from your /wp-admin/ called varnish caching. When there are features that don't work with varnish caching, we normally exclude the page with this feature from caching. Since you're trying to password protect the entire site, and it doesn't work with caching, we would have to exclude the entire site from caching. Not having caching on the homepage, nerveless the entire site, greatly reduces the benefits you receive with our hosting and increase the server resource usage.