Heat oven to 350°F and arrange rack in the middle. Grease and flour a 9-inch loaf pan and set aside.
Whisk together flour, baking powder, and salt in a medium bowl.
Combine coconut oil and sugar in the bowl of a stand mixer and beat with the paddle attachment until fluffy, about 4 minutes. Add eggs, one at a time, letting the first one incorporate completely before adding the next.
Scrape down the sides of the bowl, then add vanilla extract and 1 cup of the mango purée. Mix together on low until incorporated. Add dry ingredients and continue mixing on low just until combined.
Scrape the batter into the pan and smooth the top. Bake until a toothpick inserted in the center comes out clean, about 50-60 minutes.
Let cake cool 15 minutes in the pan, then run a butter knife between the cake and the pan to release it and turn it out on to a wire rack right side up. Let cool at least an hour before topping with the glaze.
While the cake is cooling, combine remaining mango purée and strawberry purée with the powdered sugar in a small saucepan. Cook over medium heat until thickened slightly.
Spoon over the cake and let set up for at least 15 minutes before slicing and serving. Serve any leftover glaze on the side.