The cost reduction applies only to generic mana in the cost of the activated ability. It can't reduce the {W} requirement.

Each Shrine has an ability that counts the number of Shrines you control. These abilities include the Shrine they're printed on.

Shrines count only enchantments with the subtype Shrine. Other cards with “shrine” in their name (such as Jungle Shrine, Luxa River Shrine, and Nantuko Shrine) don't count.