Frank Herbert wrote the anti-AI "Butlerian Jihad" into Dune lore to explain why the far-flung future Empire of the Known Universe still needed humans to fly ships, fight wars and do complex mathematical calculations when even in the 1950s it was obvious that robots/computers/AI would soon be able to do those things much better.
But as far as I am aware, there is nothing in the Elite canon lore saying that AIs were actually built and went rogue, thus causing Humans to stop using them (which is a quick one-line summary of the Butlerian Jihad). We have the story of Jaques the cyborg soldier turned bartender and space station owner, Elite's version of the Six Million Dollar Man, so clearly the Federation at least should have the technology to make semi-sentient AIs.
Perhaps the ED cultures have avoided robots for Asimovian reasons: the public and governments feared and distrusted their use, so none were ever built past the prototype stage. We built a few of them, to prove we could, then discovered that we couldn't actually trust them to do anything for us.
Tied in with this could be ethical concerns: perhaps the culture of the future decided it would be unethical to create a human-level artificial intelligence, then place it in a box and force it to coordinate your air traffic control, or fight your wars, or to cook your meals, or to regularly feed your cat. The Federation - the power most likely to have the tech to make AIs - condemns slavery in all forms and creating an AI specifically to force it to do menial or dangerous tasks might be classified as a form of slavery. This could at least be the public reason why AIs are not developed, even if the real reasons are more sinister.
If there is a pan-galactic anti-AI secret pact, I would expect that, historically, the INRA would have been the ones who have policed it, being the only known transnational military agency tasked with defending humanity as a whole. The Alliance is not a part of or contributor towards the INRA and has actively opposed INRA activity in the past, particularly around the Thargoid case. Frankly, I think the Alliance is still too young to have demonstrated a formal position on the issue.