First, sorry if this post is somewhat misplaced - perhaps it should be in suggestions? Mods, feel free to delete or move, or point me to the right thread.
I want to point out that it isn't just passwords; Mozilla fairly recently updated Thunderbird to share more components with Firefox - they now use the same rendering engine and, apparently, cache location. I don't know what else they now share, but the point is that they used to be more isolated from each other, and Mozilla intentionally changed Thunderbird to "better align" it with FF. I'm sure it makes sense to their developers and even to users, to a degree.
Now, with the most recent versions of FF and TB, I have problems with CCleaner pulling the cache out from under TB if I run CCleaner with TB open - particularly images in mail messages or RSS feeds, and Thunderbird does not seem to go back to the web for them. (Yeah, that sounds like a Mozilla issue to me, but here we are.) Previously, CCleaner would warn you if you ran it manually (but not with a recycle bin right-click, etc.) while Firefox was running. Perhaps it now needs to do the same with Thunderbird, for the same reasons?
There may be work-arounds but, in the short term, I think that understanding the issue is just as important. If it can first be reliably detected, that's often a good part of the battle.