Bring 4 quarts of water to a boil in a large pot over high heat. Add the rice and salt and cook, stirring occasionally, for 15 minutes.

Add the quinoa to the pot and continue to cook until both grains are tender, about 12 to 14 minutes.

Drain the rice-quinoa mixture through a fine-mesh strainer and spread it into an even layer on a rimmed baking sheet. Drizzle with 2 tablespoons of the lime juice and let cool completely, about 20 minutes—this ensures the grains stay distinct and firm.

Cut away the peel and white pith from the oranges using a sharp knife. Holding the fruit over a bowl to catch any juices, slice between the membranes to release the segments, then cut each segment in half crosswise. Squeeze the remaining membranes to collect 2 tablespoons of orange juice in the bowl.

Whisk the collected orange juice, the remaining tablespoon of lime juice, shallot, minced cilantro, and red pepper flakes in a large bowl. Whisking constantly, slowly drizzle in the oil until the dressing is emulsified. Season with salt and pepper to taste.

Add the cooled rice-quinoa mixture, chopped dates, orange segments, and the whole cilantro leaves to the bowl and toss gently to combine. Season with additional salt and pepper to taste and serve.