Combine the shredded green cabbage, purple cabbage, and carrots in a large bowl. Mix them together until they are evenly distributed, creating a colorful and crunchy base.

Whisk the mayonnaise, apple cider vinegar, sugar, salt, black pepper, and celery seeds (if using) together in a separate bowl.

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

Chill in the refrigerator for at least 30 minutes before serving.