The Aussie usage of "mufti day" probably came from the military. It was definitely in use in the 1970s and 1980s and early 1990s. Don't know about 21st-century usage; I'm not connected with high schools in a meaningful way any more.
But you're right, the increased awareness of Muslim traditions and terminology in English-speaking countries might make it seem politically incorrect. You'd have a lexicographical and etymological education project on your hands!
Yes, I like that, frindley. I didn't know the word in this context. I'll start using it and see if it I can get into common useage at my daughter's school here in England. I'll probably get told it's not PC!!!