By using Private Browsing mode in your browser (all modern web browsers do this, Facebook cannot permanently save a tracking cookie to your computer, nor can they read your history or other cookies. It’s as if someone was connecting to them from a computer that had never connected to any other site, from their point of view. So you can create a new account with bogus name, address, etc., information entirely separate from your ‘real’ account if you have one and you can link it to an a casually anonymous email or even a throwaway forwarding account to get past the authentication crap. Once you do that, you can then post anonymously (again, in Private Browsing mode) on any site that requires Facebook logins and exposes names and such to the public.
Thank you very very much.