Any site which requires people to log in MUST use cookies, otherwise their server wouldn't know who was posting. (i.e. without cookies, if you wanted to post lots of times on a Chatterbank thread you'd have to append your log-in details to every single post you submitted).
The additional (tracking) cookies used by AB are needed as part of the system that funds the site. However, irrespective of whether you've given permission for them or not, many (most?) browsers block tracking by default anyway. (e.g. Firefox has 'tracking protection' turned on in its 'fresh out of the box' state). So if you use such a browser then those cookies are effectively disabled anyway.
AB is actually being extremely generous in permitting people to use it with adblockers enabled. (They clearly don't approve of it but they've not sought to prevent it). Many websites (notably those of local newspapers) won't allow you access at all unless you disable your adblocker. Further, many of them use picture galleries to illustrate stories, which won't load unless you also disable tracking prevention in your browser.
I find it odd that people object to their browsing habits being tracked but often don't seem to mind that Google tracks their physical location from their phones.