Kombucha is generally not recommended for nursing / pregnant moms, in case a potential healing crisis in which the mother’s symptoms may affect the baby as their immune system is not fully developed / strong yet.
However, this is just precaution only. It is alright if the nursing mother still wishes to take kombucha, especially if she has consumed other fermented foods before such as kimchi, yogurt, sauerkraut etc. as the body is more adapted to the bacterial load. Also she can dilute with water first and consume small amounts like 50-100ml to see how she feels. If everything is alright, then she can gradually increase consumption.