This relates to the desktop app on Windows. Several of the playlists listed on my Public Profile page are private and should not be listed.
As you can see from the image below, the drop-down menu for a playlist on this page includes an "Add to profile" option. This implies that it is not already on the profile and therefore not already public. This playlist remains as such after navigating to other pages or restarting the app.
If I click the "Add to profile" option it is replaced with a "Remove from profile" option. If I then click on the "Remove from profile" option then navigate away from the page and then back to it, the playlist is then removed from the page.