When Dune was written, the most terrifying computers out there were conceptually like HAL 9000: a machine that acts like a human. The battle with HAL isn't a balls to the wall sci-fi war against AI but a man trying to survive a malfunctioning machine on which there is too much reliance. That's not even subtext, HAL straight up is given too much conflicting responsibility and fails because it is a machine. And while 2001 came out after Dune, it's kind of a useful mark of the zeitgeist at the time towards computers.

The Butlerian Jihad is straightforwardly based on Darwin Among The Machines, an essay by Samuel Butler, which more or less argues we should be anprims because otherwise we constantly cede responsibility and power to machines and eventually will find ourselves inferior to them. It's not a "Ooh, Skynet" argument like Herbert's son made it, it's a human supremacy over nature argument. What are we if not supreme over all other forms? What is the hierarchy if humans aren't at the top?

Herbert, as a world building exercise because computers are boring, decided to have a reason there aren't any smart computers in Dune. Of course they still have Turing machines, or otherwise nobody could fly a thopter or operate a spice harvester or dew factory or the myriad spacecraft. But being smart is reserved for humans and having giant brains is reserved for Mentats, and even they're shown to be very fallible. Piter dies because he didn't think the Duke would be a threat, Hawat fails as the Duke's Mentat because he couldn't imagine Yueh was the traitor until his dying breath.