Here are the different types of male hats and the requirements to wear them:

Holy Cap: For male Priests with 11 or more Insights. Purple velvet with gold embroidery and ermine trim, dyed with trigonelle and spirulina.

Magus Chief: For male Wizards with 11 or more Insights. Crimson felt with white and gold embroidery, dyed with hyssop, paola nut and spirulina.

Magus Conical: For male Wizards with 11 or more Insights. Blue and gray felt dyed with angelica, paola nut, spirulina and capsic bark.

Holy Conical: For male Priests with 11 or more Insights. Blue and gray felt dyed with angelica, paola nut, spirulina and capsic bark.

Holy Chief: For male Priests with 11 or more Insights. Crimson felt with white and gold embroidery, dyed with hyssop, paola nut and spirulina.

Cap of Danaan: Can be gained by any male Aisling able to take the quest which starts with a young boy in the upstairs rooms of Piet Inn. After acquisition it can be consecrated to the patron deity of that Aisling.