It's annoying to me too. I can't just hide all my tray icons because I need some of them, and the red O makes my desktop/theme look crappy since all the other icons are white (using GNOME with Orta theme + Faenza icons).
Yes, I understand that. You can configure the system tray to hide icons from specific programs. That way you have every icon except for Opera. The program need not include an option to hide it.
There is no "properties" setting for the Notification Area applet in Gnome (at least in version 2.32.0.2, which is what ships with Fedora 14), which is what the commenter you responded to said he was using.
Right click > Properties