Honestly speaking your better off just visiting the sites. Whats wrong with going right to Yahoo.com and checking your mail?
and what's wrong with using an email client
... you don't solve issues by avoiding them, troubleshooting is the key word here ; + there's a mail shield in this AV suite (remember, you're on Avast forums) and it's meant to be used for those who want to. Especially if the guy has two accounts, the case here
@ the OP: I don't use yahoo mail but okay, if no ssl is required on POP and SMTP, leave the required server settings as is in Thunderbird and check what the mail shield detected and did >>> go to mail shield advanced panel, ssl accounts section and if you see that Avast is redirecting to ssl ports, undo that, ie set to "none" , POP on 110 and SMTP on 25.
Now if ssl is required, check that your server settings in Thunderbird are POP/143 and SMTP to 25; then go to the mail shield advanced settings again and check that POP is redirected to 995 and SMTP to 465 (ssl) or 587(TLS).
Guys in a general way on this forum, avoid advising someone who has issues with the mail shield to forget about it and jump to the browser interface or use a mail notifier just because it's easy, and because you can't help. These posts are useless, and I find more and more of them.
This being said, there's a tutorial on Avast main site about the mail shield, + tens of threads where the mail shield is related, read and browse