You can’t. Earlier versions of FF used to allow you to do this via GTK, but not anymore it seems. Note that the application itself is only allowed to change the class – and it isn’t allowed to be changed post window mapping.
Style Navigator StartsOnPage foo DestroyModuleConfig a:* *a: add_window SomeFunc AddToFunc StartFunction I Module FvwmEvent a DestroyFunc SomeFunc AddToFunc SomeFunc + I ThisWindow (!Navigator) Break + I Any (Navigator) Style ....
– Thomas Adam