Make the dressing: In a small bowl or jar, whisk together rice vinegar, soy sauce, sesame oil, honey, ginger, and garlic. Slowly drizzle in the neutral oil while whisking until emulsified. Set aside.
Prep the veggies: In a large bowl, combine green cabbage, purple cabbage, carrot, bell pepper, green onions, and cilantro. Toss to mix.
Add the chicken: Add the shredded chicken to the bowl with the veggies. Pour the dressing over everything and toss well to coat.
Chill (optional but recommended): Cover and refrigerate for at least 30 minutes to let flavors meld.
Serve: Just before serving, top with crispy wonton strips or almonds for crunch. Toss again and enjoy.