For those unfamiliar the Dune series, the Butlerian Jihad was a crusade against “thinking machines”. Ultimately computers, and intelligent or thinking machines, even down to calculators are destroyed and banned. Humans who are trained in complex mental maths become known as Mentats, a sort of human computer. Just, uhh, leave all that shit on Bene Tleilax, with their Axalotl Tanks out of it.
Edit: had wrong planet name. IX -> Bene Tleilax
real talk; the answer is that the Mechanicus are too powerful for the Imperium to actually fuck with. For one, they were an already established and very strong empire on Mars while the Emperor was just getting humanity back together after a great collapse on Earth, so they negotiated the alliance from a position of power. For two, the Imperium gets every gun, every ship, every tank, every drop pod, every Titan, literally everything other than I think food and manpower for their armies from the Mechanicus. If you wanna start investingating their “definitely not-AI,” you gotta be prepared to have your shipments of Leman Russes to suddenly start getting lost.