Anonymous access not working properly

I am using Grafana V5.3.4 and configured it for anonymous access. Unauthorized access works from Chrome on my notebook. When I try to access Grafana through Safari on the same notebook the browser is redirected to a login page. The same happens when I try to access Grafana from a different computer with Chrome or Firefox.
I have no glue what to look for, since obviously the anonymous access seems to be working in principle. Any help is highly appreciated.