Cover thy knees and shoulders!
When entering the grotto or the monastery, just like most churches or religious buildings in Greece, make sure your knees and shoulders are covered! I had shorts on and had to wrap a towel around my waist in order to keep my knees from showing. The local people will definitely frown upon that if they see you exposing those areas in a religious place!
White walls, stone ornaments
In these dodecanese islands, there are no more white & blue villages (as in the Cyclades), they are more white & brown, as they are built mainly in stone, though the walls keep the white color.