I think Spotify should add privacy settings for playlists so that the playlist creator has the option of only having certain users being able to view the playlist. I think it would really help because some people may have playlists that they want to keep "private," only wanting certain people to be able to listen to the songs on the playlists. Plus, it would probably solve the issue that some users have with people "stealing playlists," taking all the songs from someone else's playlist and adding them to their own playlist.
You can always select "Make Secret" in the playlist options, just right click on the playlist you don't want to be shown on your profile and click on "Make Secret". On mobile tap on the 3 dots menu. It'll also won't show the playlist in your "Friend Feed". It'll be visible only to users which you give the link to the playlist.
In addition to that you can go in your settings and uncheck "Automatically make new playlists public", so every new playlist you make will be only visible to you.
You may also be interested in this idea for password protected folders, so even people who use your computer/phone will not be able to open it.