AFAIK, it uses its own alien GUI, not Reaction, not MUI, not anything else native on any desktop platform...
There, I fixed it for you

Mozilla has had it's own abstract UI components since, well, forever. On some systems, these can be wrapped around the native GUI and improve the sense of integration (more often than not, it's just themed that way). BOOPSI, with it's slightly unusual dispatch engine and support for runtime-defined classes etc. isn't always the easiest UI to wrap around.