Bad news. I tried different things to avoid the icon's transparent parts getting messed up and none of them worked.
Not even transparent PNGs avoid the bug and so I believe that it's related to how wxWidgets draws the icon.
Currently there is one last thing I would like to try: compile FileZilla (also uses wxTaskBarIcon), give it our icon and check whether it gets messed up. I am almost completely sure it will.

EDIT:
Same goes for FileZilla. The icon has a wrong background in the taskbar but looks OK in the toolbar. All icons are loaded the same way inside the code.

The FileZilla crew avoided the taskbar issue by using a square icon that has no transparency.
