Your comment very much implies a strong link between the two however. That you then switch from data centres to factories is also a shift that is not related to the discussion at hand.
Personally, everything I've read on the issue indicates that the water usage, for a product that I hear mentioned daily by people in the street, is insignificant.
I have many qualms with AI, mainly about the politics of AI labs and its effects on inequality, and I am active in this field. But I see its environmental costs as a weak argument and don't use it, despite of how receptive people that I try to convince are to it: it uses much less energy, harms many fewer animals, and serves more of a purpose than animal agriculture, so I prefer to move my environmental actions towards that.