Simply put... in some parts of Europe, women in tank-tops and men in shorts are not allowed in Cathedrals. What is appropriate in Japan's Shrines and Temples and specifically when on a temple stay at Koya-san? Thank you.
On Mt Koya you will be staying in a temple so you can dress casually. For the morning service you should dress in what you will wear for the day though some people wear their PJs.