Personally I'm using Firefox 66.0.2, I believe it to be the latest release/stable (non beta) version.
It does the same even if I try disabling web shields, HTTPS scanning...or even all shields.
Later addition:
Reinstalling Firefox doesn't help. If you install it from scratch (no profiles or private data) of course it is OK, but if you enable Master password protection, it immediately requests for the password upon every restart.
So the question is, why is Avast trying to access this on every start ?