Ah! I finally figured out why my #Thunderbird wasn't working with the new #Yahoo! Mail #authentication system.

It turns out, I had "accept cookies" turned off in Thunderbird, and while I had exceptions set for Yahoo, the exceptions were only for http, not https. Unlike when I add exceptions by domain in #Firefox, Thunderbird doesn't automatically allow from both http and https connections.

Adding the same exceptions for https did the trick, and now I can access my Yahoo! Mail again.