If you're asking if the Opera browser in itself can be trusted, then the answer is Yes as far as I am concerned. The Opera browser is well-known and extensively used, and relies on the Chromium engine.
However, if your system is compromised by banking malware - note that Norton is not full-proof like all AVs - which can work under your conditions (e.g. the service you're using, how you're performing the transaction, etc.) then you can be affected. Remember though, a malicious extension can steal data as well (e.g. login credentials) or force-data (e.g. switch Bitcoin addresses or PayPal e-mail addresses and so forth).
I recommend you use a dedicated machine if you feel you need to as
@upnorth has mentioned for you. If you do not have a dedicated machine for it and feel you really need an extra layer, consider a sandbox for the browser (e.g. Sandboxie) or a Virtual Machine (which you can use for the banking transaction prior to wiping with a snapshot).