If you want to remain any kind of anonymous, it means logging into each facebook login-enabled site with a new, fresh fb account. Using one trash account might stop them from linking things to your 'real identity' (such as fb perceives it), but it still lets them link all of your activities together and build a profile. Persona linking from there isn't hard, based on usernames or email addresses used (see pipl and similar for examples of casual, publicly available version of these tools). But even if there's no persona/pseudonym linking algo going on, you're still being 'tracked'. It's not fully anonymous.

Unless you clear your Facebook cookies each time you log out.

There are also in-browser tools that prevent cookies from being sent to third parties.