Wow, the MUI-lovers are out in force today :-(
ReAction is the official AmigaOS GUI, this applies to both 3.x and 4.x. If AROS and MOS don't support then that is a lack in those OSes. If those OSes didn't support eg. menus, would there be suggestions along the lines of "don't use menus"?
ReAction software can run under MOS, it's just a matter of the relevant classes being omitted from the MOS CD for some reason. As for AROS, if/when the 68K emulation ever gets done then ReAction classes will be usable under that too. As it stands, AROS is missing huge chunks of functionality and isn't ready for prime time anyway.
MUI is a third-party hack and rather slow and ugly IMHO, requiring many extra files and not giving any benefit over ReAction. Another case of reinventing the wheel for no real purpose and forcing users to go download and install extra packages instead of using what is already present in the OS.
ReAction is based on ClassAct from Finale Development and was renamed and added to Amiga OS in version 3.5.
MUI was available 7 years before that.