In a large mixing bowl, combine the shredded green cabbage, shredded carrots, and shredded purple cabbage (if using).

In a separate bowl, whisk together the mayonnaise, apple cider vinegar, sugar, celery seed, salt, and black pepper until smooth.

Pour the dressing over the cabbage mixture and toss until well combined.

Cover and refrigerate for at least 30 minutes before serving to allow flavors to meld.