Redirect bug when NOT logged in

Dear all,

I have a WordPress site at hegyvidekkozpont.hu

We have found out that it has a very serious bug that only exists when the visitor is not logged in (99% of the time, as I’m the only registered user).

On this page there are several post items:
http://hegyvidekkozpont.hu/programok/

However, when I click on a link to read more, it redirects me to the right page (single-events.php). When I log out (so I’m clicking as a regular visitor) it redirects to a different template.

I have the following plugins installed:
– WP-Types
– ACF
– Gravity Forms
– WPML

Any ideas what might cause the problem? I have tried flushing the permalinks by resetting the structure, tried different template files and still no results.