Quarter the cabbage through the core, and then cut out the core. Cut each quarter crosswise in half and finely shred. Place the shredded cabbage in a very large bowl (you will have a 4 to 6 cups). Add the shredded carrot and apple to the cabbage and toss to mix.
In a separate bowl, stir the mayonnaise, kombucha, kefir, lemon juice, salt, pepper, and coconut sugar together.
Pour the dressing over the cabbage, apple, and carrot then mix well. Eat right away or let it sit in the refrigerator for about an hour to let the flavors mingle and the cabbage to soften.