I suspected as much, thank you tufuzay and leocg.

I have Opera 36.0.2130.80 installed, which the about page states is up to date. However, at least 20-35% of the websites visited now result in the following error message:

This site can’t provide a secure connection

www.insertwebsitehere.com uses an unsupported protocol.
The client and server don't support a common SSL protocol version or cipher suite. This is likely to be             caused when the server needs RC4, which is no longer considered secure.  

The number of sites this is a problem at seems to be growing. Replacing the https with http does not work, it simply forwards to the https and results in the error message above. Tweaking my proxy security settings has not helped either. What was once annoying is becoming increasingly inconvenient. I'm not really sure what to try next.

Constructive suggestions would be appreciated.