Remove peel and white pith from oranges.
Working over a medium bowl to catch juices and using a small sharp knife, cut between membranes to release orange segments into bowl.
Squeeze membranes over bowl to release any juices.
Strain juices through a fine-mesh sieve into a small bowl; reserve orange segments.
Add 1/4 cup lime juice, oil, and fish sauce (if using) to bowl with orange juice; whisk to blend.
Set dressing aside.
Bring rice and 2 3/4 cups water to a boil in a large saucepan.
Season lightly with salt.
Cover, reduce heat to low, and simmer until all liquid is absorbed and rice is tender, about 25 minutes.
Remove pan from heat and let stand, covered, for 15 minutes.
Spread out rice on a rimmed baking sheet, drizzle with dressing, and season lightly with salt; let cool.
Place mangoes and remaining ingredients in a large bowl.
Add rice and toss gently to combine. Season lightly with salt and more lime juice, if desired.