Heat 2-1/2 cups water and 1 t. salt in medium saucepan to boiling. Add rice and stir. Reduce heat to low; cook covered until water is absorbed, 10-12 minutes. Let stand covered 10 minutes.
Meanwhile, toast pine nuts in medium skillet over medium heat, shaking pan frequently, until golden brown, 5-7 minutes. Transfer to small bowl; let cool.
Make dressing: Whisk oil, lime juice, mayonnaise, mustard, remaining 1 t. salt, and pepper to taste in small bowl. Pour half the dressing over warm rice and toss to coat. Add mushrooms, peppers, scallions, and half the cilantro; toss to combine. Let stand covered at room temperature 1 hour.
When ready to serve rice salad, add remaining dressing and cilantro and the pine nuts; toss to combine.