Preheat oven to 350°F (175°C). Lightly grease or line a muffin tin with parchment liners.
In a mixing bowl, cream the butter and sugar for the crust until light and fluffy. Mix in flour and salt until combined and crumbly.
Press the dough into the bottoms of the muffin tin cups to form a base. Set aside.
In a small saucepan over medium heat, cook the chopped rhubarb, sugar, and lemon juice until soft and slightly thickened (about 5–7 minutes). Set aside to cool slightly.
In another bowl, whisk egg whites until frothy. Stir in sugar, vanilla, salt, and shredded coconut until well combined.
Spoon a teaspoon of rhubarb mixture onto each crust base.
Top with a generous spoonful of the coconut mixture, gently pressing it down to adhere.
Bake for 20–25 minutes, or until the tops are golden brown.
Let tarts cool completely before removing from the tin.