The ingredients for the non-dairy peach Chobani yogurt are: cultured coconut blend (water, coconut, tapioca flour, agar, cultures), cane sugar, peaches, water, chicory root fiber, lemon juice concentrate, natural flavor, fruit pectin, fruit and vegetable juice concentrate (for color), locust bean gum, Manufactured in a facility that also handles milk.
Here is information about other non dairy yogurts:
https://www.vrg.org/nutshell/Guide_to_Vegan_Yogurt_2017.pdf