But that's sort of the point, isn't it? It's generous even to call "skeptics" a group. There are just "people who have skepticism about X," many of whom have skepticism for wildly different reasons — many of them
bad reasons — and therefore are not convinced by
good evidence.
AI will produce whatever evidence a person needs in order to shore up their own "skeptical" beliefs. Same problem as social media, where finding 1000 other people who share your fringe beliefs looks like compelling evidence for your belief being true. Just now it's on-demand, hyper-personalized, responsive to your own doubts, and there's no chance of you realizing "ah, my comrades on the other end of the tube are actually idiots!"
I'd bet an AI product that tells a flat earther that "it's an open question" will be much more successful than an AI product that attempts to dispel that myth. That is, at least until an AI can effectively convince people away from their beliefs, which almost certainly will not happen via "calmly providing solid logical evidence," given that this is not usually an effective vector for persuasion anyway. Now you've got a new problem, which is a technology capable of convincing people of all sorts of insane things.