You can only add favorites when you are a registered user and when you are logged in in your account.
But when your not logged in in your account you also see the favorite icon on the listing and when you click on it you see the text "listing has been added to your favorites" only nothing happends.

Maybe it would be better to only show the favorite icon when you are logged in or make the click action on the favorite icon only work when you are logged in and otherwise show a message like "you need a account in order to mark favorites".

@vansebas
That is correct, as list of favorited listings is in plugin under user folder that does not allow non-logged users to get there.

Yeah that is working lovely, but wouldn't it be better to only show the favorite icon on the listing only for logged in users?

I do not see reason for that. For nonlogged users, their id is created and stored in cookies and they can use basic functions of plugin