Games

the Imperium's full(sans Cawl) Butlerian Jihad position

The Imperium is a bit weird in that regard because they still clearly use machine intelligences, they just totemically house them in old human skulls so they can pretend it's just a post-mortem augmetic modification to a person instead of something fully mechanical. Housing them in human remains may also diegetically help protect against warp corruption, since it means they're being housed in relics that people believe to be inherently pure. There's also the reading of machine spirits in general as AIs of varying levels, which shows up in some stories.

The hypocrisy and idiosyncracy is part of the point, imo. The Imperium is an inversion of expectations, cliches, and even its own themes in a lot of ways: it's monolithic, unifying, and intolerant of any deviation from its monoculture on the surface, but actually extremely fragmented and autarkic, highly varied, and too overwhelmed to care about anything but the biggest "don't make daemons, collaborate with outside states, or stop paying your taxes" rules; it's completely inflexible and rigid in its application of its rules, except its enforcers just kind of do whatever they feel like and constantly decide whether a rule really mattered or not on the fly; they're embattled and fragile and constantly being overwhelmed on the surface, except the one truly solid and unyielding thing about them is their endless war machine and how they're dug in deep everywhere they touch; etc. Denouncing AI while actually making heavy use of it in specially permitted forms is extremely on brand for them.