Mix flour, baking soda, and salt together in a bowl.
Combine white sugar, brown sugar, coconut oil, and butter in a separate bowl; mix until creamy. Beat in persimmon pulp. Add eggs and vanilla extract; beat until well combined, scraping sides of the bowl occasionally.
Stir flour mixture into persimmon mixture by hand until thoroughly combined. Add dates and oats; mix dough well.
Drop dough by rounded teaspoonfuls onto an ungreased baking sheet, about 2 inches apart.
Bake in the preheated oven until golden brown, 10 to 12 minutes. Cool briefly; transfer to a wire rack to cool completely, about 10 minutes.