In fact I didn’t disable SSL in mail accounts in Thunderbird with the older version of Avast - there was a warning message of Avast about that (don’t remember the exact phrasing) but I selected to ignore this and not check my SSL mail account in Avast. But in Avast 8 it was no more possible, as when I disabled SSL mail account checking in Avast (to not have to override the mail provider certificates by the avast ones) the e-mails were not downloaded at all, so I had to enable SSL mail checking back in Avast and override the mail provider certificates by the Avast ones (I suppose Avast uses the “man in the middle” technique to be able to check SSL e-mails). But after uninstalling Avast the situation seems to be the same like when I disabled the SSL mail checking in Avast - Thunderbird seems to try to connect to the mail accounts (shows e.g. “Connecting to pop.gmail.com”), but then the connection ends without downloading any e-mail or any error message.
The funny thing is that even when I remove all stored passwords in Thunderbird, it doesn’t ask for the password. Just drops the connection without any error message.