While I don’t use white sugar in my cooking or baking, the experts over at Cultures For Health say it is required for kombucha and it should not be replaced or substituted. During fermentation, the white sugar reacts with the tea and kombucha culture to produce acetic, lactic and glucuronic acid.
Adapted from Nourishing Traditions
Find it online: https://deliciouslyorganic.net/flavored-kombucha-recipe/