In religious communities we would call such an attitude scrupulosity. It refers to a sort of religious OCD, a paralyzing fixation on the rules and a demand for unrealistic standards of perfection.
According to Christian teaching, such an attitude comes from a lack of faith. A lack of belief that God is ultimately in control, and an understanding that for all the imperfections and flaws that we as humans inevitably bring to the table, god can still work through those imperfections.
I'm not sure there's an existing "Christian teaching" on "should I use an AI chatbot that's highly likely to make shit up as a proselytizing tool"?