I am posting this in case anyone will encounter this problem. I also reported a potential bug about that. (see here: https://github.com/craftcms/cms/issues)
When you start to suddenly get redirection loops with HTTP-302 redirects to our own page, you might want to check your loginPath value in general.php.
After we spent hours investigating into the usual .htaccess and other places for redirection loops, we eventually figured out, that loginPath set to '/' will cause that behaviour.
We wanted to redirect users to the homepage if they were not logged in and tried to access a page that required a login.
Our setting was:
'loginPath' => '/'
which proved to cause the redirection loop.
The correct setting instead was:
'loginPath' => ''
I hope this saves somebody else from future pain :)