Hi, I have a new iMac with El Capitan 10.11.2 and I downloaded Opera, it is my browser of choice and I am using Opera 34.0 no issues with it so it is not a fundamental issue Opera and OS X 10.11.2.
You say you have clean installed the Opera, was there a previous version loaded, did you run a clean utility such as Ccleaner, reboot then install Opera? Just a thought.