i cant think of anything in the update that would do that

if you go to the article manager are they still set with the correct access level?
if they are then please check with one of the default templates - if it works thenit is an error in a template override

Cannot replicate

• installed Joomla 3.7.1
• Created menu link to featured articles
• made articles featured and Registered
• Clicked menu link to featured articles when logged out (public)
• No articles shown.

switched to protostar and beez3, still the same featured articles as guest AND registered appear on start page

switched to protostar and beez3, still the same featured articles as guest AND registered appear on start page
Have you tried from a different browser? Perhaps you have "Shared Sessions" enabled when you didn't previously, and it's just because you're logged in to the admin.

Please see this

http://prntscr.com/f9e8mu

settings as featured articles for both of them
http://prntscr.com/f9eagh

can be seen on www.talking-business.de/de

I had a look at the website. The "Show Unauthorised Links" option was set to yes. And since all the article content was in the intro text we were seeing the whole article. No idea why it was working on 3.6.5, but it actually should have been the same...

That makes perfect sense and iirc this is because of a bug fix to correct the behaviour to the one you have now. I am closing this now.