Prepare the dressing by stirring together the mayonnaise, Greek yogurt, apple cider vinegar, honey, and salt.
Remove the core from the cabbage, then shred the leaves into very thin strips. Peel the carrot, then shred it using a large holed cheese grater. Wash the apple well, slice it in half, then remove the core with a melon baller or sharp spoon. Use the cheese grater to shred the apple. Press the shredded apple between a couple pieces of paper towel to absorb the excess juice.
Place the shredded cabbage, carrot, apple, and raisins in a large bowl. Add the dressing over top, then stir until everything is evenly coated in dressing. Serve immediately.