I reported this to AgileBits yesterday and after doing some diagnostics with their team they reported:
"All versions of Opera are now signed with a new certificate, one not known to 1Password 6. As a result 1Password cannot verify the browser code signature and when it can't it will refuse to connect. This will require an update to 1Password as the known certificates is a hardcoded list inside 1Password. I apologise as it means you won't be able to use Opera with 1Password for the moment."
Going to file a ticket with Opera.