The Guardian published this Reuters photo of a Holy Week procession in Seville, Spain. In fact, Wikipedia also noted the comparison:
Origins of the Ku Klux Klan Costume
The origins of the use of the costume are unclear. Although the organization has no relationship with Spain, the contemporary white gown with a cone hat follows the Spanish Roman Catholic "Nazareno" tradition. Such garments have been traditionally used in festivities such as Holy Week, symbolizing the act of penance. In Spain and its former colonies, the pointed hat is called "Capirote".