To make the dressing, combine the olive oil, lime juice, honey, poppy seeds, cider vinegar, mustard, and cayenne pepper in a medium jar with a tight-fitting lid. Shake well until thickened. Season with salt and pepper.
To make the salad, combine the mangoes, avocados, cilantro, and half of the pistachios in a medium bowl. Add the dressing and toss well to coat.
Put the spinach in a large serving bowl and top with mango-avocado mixture. Toss gently until combined. Sprinkle with the lime zest and the remaining pistachios. Serve immediately.