I can see the entries for your attempts to log on, but you are using the same IP address as in this post and I can’t see any ban on this IP so it is somewhat strange.
Are there any differences in how you logon with Firefox and Chrome (such as logging on using Google Account, etc.) ?
Is this Google Chrome or some other variant of Chromium ?
Are you using any addons in Firefox that might somehow impact on the logon?
Try running firefox without addons, safe mode does that make a difference ?
Its certainly a bit weird as my browser of choice is Firefox and I haven’t had this issue on any of my systems.
However I do use CookieMonster on my XP desktop with an old version of Firefox ESR and I have that allow Cookies for forum.avast.com I haven’t set any Exceptions. I just wonder if you have restricted it a bit too much, e.g. to board=2, whilst this is the main board, I don’t know if other boards General for one.
You did have several ban entries relating to board=2.0 there were others such as forum.avast.com and others.
That said the login would I have thought been for forum.avast.com/index.php and the validation of username and password would be different again.
Hopefully your exception will work across the board (excuse the terrible pun), without further issue.