I'm not buying it. ISPs have had access to way more request data for years and haven't had success selling advertising. Site owners, privacy advocates and net neutrality folks would freak out and shut it down in a heart beat.

More especially since they hijack HTTPS sessions. I always thought that playing MITM and caching secure sessions created a strong incentive to behave badly.

They don't do that:

from

http://labs.opera.com/news/2009/03/13/

Your privacy is important

Even when Turbo is enabled, encrypted traffic does not go through our compression servers. This means that when you are on a SSL site, we bypass these traffic and let you communicate with the SSL site directly. Opera generates statistics of the usage of Opera Turbo, but these are aggregated numbers and no information can be linked to a single user. Opera does not store any users’ private information.

Presumably that is a feature of the desktop version?

http://www.opera.com/mobile/help/faq/#connection

"Is there any end-to-end security between my handset and — for example — paypal.com or my bank?"

"Opera Mini uses a transcoder server to translate HTML/CSS/JavaScript into a more compact format. It will also shrink any images to fit the screen of your handset. This translation step makes Opera Mini fast, small, and also very cheap to use. To be able to do this translation, the Opera Mini server needs to have access to the unencrypted version of the webpage. Therefore no end-to-end encryption between the client and the remote web server is possible.

If you need full end-to-end encryption, you should use a full web browser such as Opera Mobile."

Turbo and Mini aren't the same thing; Turbo mostly just compresses everything and lossily recompresses images to make them smaller, while Mini outright doesn't have a local HTML rendering engine.

Opera Mini tells you about that (and that the connection isn't actually protected) and discourage you from continue when you try to enter any https site.

"they hijack HTTPS sessions"

Trolling much? They aren't hijacking anything. Opera Mini is a thin client (which lets it run on just about any phone, including old and crappy ones), so they have no choice but to pass everything through the rendering engine on their servers.