Make the Dressing: In a large bowl, combine the lime juice, white wine vinegar, and salt. Stir until the salt begins to dissolve.
Add the Vegetables: Add the thinly sliced cabbage, grated carrots, red onion, and chopped cilantro to the bowl.
Toss and Rest: Toss well to ensure all the vegetables are evenly coated with the dressing. Let the slaw sit for at least 10 minutes before serving to allow the flavors to meld and the cabbage to soften slightly.
Serve: Toss once more before serving and adjust seasoning if needed.