I have the issue at home: Opera 40 up-to-date running on OS X 10.9, failing to sign in and sync. It has been broken since July 2016 or earlier.
The opera://sync-internals page reports an unrecoverable error (BackendInitialize failure), which seems related to the Chrome engine. Maybe the local data have been corrupted in some way, however I don't know how to repair that.
Checking on <sync.opera.com/web/>, remote data are OK. At work I use Opera 40 running on Win7, and this one signs in and syncs alright.