Found out the reason why the Opera splash plays at every startup for some people and how to disable it.
Opera used to store it's preferences in "[profile_folder]\Preferences" but in a recent update changed the location to "[profile_folder]\Default\Preferences" without removing the old files.
For some reason the existence of "[profile_folder]\Preferences" is still checked and it's absence will cause the splash to be shown at every startup.
Users with newly created profile folders will see the splash every startup and users with "old" profile folders wont.
Just create an empty "Preferences" file in the root of your profile folder and the issue goes away.