I received this response from the Opera Q/A team:

The only way for this to happen is when following entry is added to your Preferences file in your profile:

"incognito": {

"mode_availability": 1

}

I do not find this in my Preferences file. Does anybody know what is wrong with my browser? (I am using Windows 7 32-bit.)

I recently tried installing and extension, and tried enabling it for private browsing. The option for enabling/disabling it for other extensions was also gone-- the extensions appear locked in the previously set settings. Do other people have this issue? Thanks!