I don't trust any "organization" to store and manage my passwords. A single subpoena to mozilla for a divorce proceeding or whatever could unleash cascading consequences upon you.
It's not really a "password manager", it uses signed assertions instead of plaintext passwords. It is similar to client certificates, but with a much better UI.
Also, in the future you probably won't even need to contact Mozilla anywhere in the process: your browser will store your certificates for you, natively.