I also just learned that Android Opera does not sync passwords anyway. At least that's mentioned in http://www.opera.com/help/account#sync.
For extra fun, I've tried multiple times to reset synchronization. The account seems to be cleared, but it's repopulated even though I don't tell Opera to log in. When I do login, I invariably get asked my password. So I can't switch back to syncing without a passphrase.
Guess I'm creating a new account—if that fails I might have to sadly give up on Opera.