and someone posts on that guestbook <img src="www.guestbook.com/index.php?logout=true"> anyone who views that page will be logged out, and that is what I need to somehow prevent

just a side note: if this is your web application you can prevent that this happens, for example by using a kind of token. I do this in one of my webapps by adding a token to every link/form that changes something on the server. see Is your web application really secure? ("CSRF"). You can reduce the risk a little bit by checking if a request was called with the method POST.
If this is not your webapp then you'd have to contact the author =)
Neither Firefox nor Opera can fully prevent you from CSRF at the moment, they both do different things to try it.
But I also wonder why mechanize would load images.