The dressing can be stored in the refrigerator for a day or two, tightly covered; whisk it until smooth before serving. Mint would be a nice alternative to basil.
Remove peels and piths from grapefruits with a sharp knife. Working over a bowl to catch juices, carefully cut between membranes to remove whole segments. In a bowl, whisk together 2 tablespoons grapefruit juice, vinegar, mustard, 1/4 teaspoon salt, 1/4 teaspoon pepper, and yogurt. Slowly drizzle in oil, whisking until combined.
Toss together greens and basil; divide evenly among 4 plates. Top with grapefruit and avocado. Drizzle with vinaigrette, sprinkle with poppy seeds, and serve.