Non-logged in (Visitors, Guests) users cannot view the listings. It says "You don't have access to this part!".

In WPL PRO you can manage guest/visitor users' access. You can block their access to single property pages, property listing pages, etc. Go to WPL->Memberships and edit Guest membership and set your desired access and click on the "Save and update all members" button.

This feature needs WPL Pro + WPL Membership add-on.

If you don't have WPL PRO, you can change guest access directly from the database->[wp_prefix]_wpl_users table. Edit id=0.