Log into WordPress and create a Post with CiviCRM content embedded. (Use the CiviCRM button to add a Profile or other such content to the post.) Mark the Post as a Private post. Then go to CiviCRM, while still logged in, and load something that has publicly viewable content in a new browser tab. (The Event HTML listing page is a nice, quick test page.) The resulting page will show Private, rather than showing the Publicly available content. Log out of WordPress/CiviCRM, then refresh the Publicly available page, and suddenly everything renders correctly. Log back in, delete the Private Post created earlier, reload the Publicly available page and it renders correctly while you are still logged in.
Here's a StackExchange discussion:
I'm unable to reproduce this on the demo site as I don't have permission to add Posts on the Demo. However, two different VM's I built exhibit the same issue.