WooThemes not working with Membership plugin

I am experiencing problems concerning WooThemes Membership premium plugin.

When I am not logged in (being nothing more but visitor), several parts of the site are missing (for example, menus). When I am logged in, the site shows up correctly.

The problem is that this happens if the plugin is installed, but not activated (or activated and proper rules are set - so, in both cases). If the plugin is completely removed, no such problems exist.