I too suffer from the same problem: some sites just won't load on Opera while they work quite fine on other browsers. I tried everything but could not get it to work.
Yesterday I tried to complete and submit a report on my State's Secretary of State (SoS) web site. No luck. The required web sites opened and worked perfectly on two other browsers. I called the SoS's office, was immediately connected to the tech help person whose first question was, "what browser are you using?" When I told him Opera, he said, "Try Firefox, Safari or Chrome. They should work."
He was right. The required sites opened on Firefox and I was able to complete and submit.
What a shame. I have learned to love Opera but this appears to be a problem that almost has me going back to Firefox. I will continue to use Opera and look forward to the problem being solved. When the first piece of advice from a site owner is to tell you to use another browser, that means the problem is one they have faced many times in the past and is probably a lot bigger than the settings on my iMac.
Opera should pay some attention to this vexing problem, if they haven't already.