We already have something like the bene gesrit with psionics (although it defintiely needs to be expanded alongside the other ascensions) and sadly the spacing guild will never happen because in stellaris faster than light travel is easy and there is no magical substance that absolutely is necessary for space travel. I do not know what the Ix and Tilaxu are though.
The Bene Gesserit are kind of a mixed ascension path (using breeding to get to psionic power), but the key point is that their in-game equivalent would have to be a group advocating psionics as a development path (perhaps pulling from the Vicky 3 Interest Group idea), and in a much more active way than "we'll give you a bit of pop happiness and influence if you do it."
As you say, the Spacing Guild wouldn't exist as it does in Dune, though it's one of those cases where the constraints of the world would change their face, if not their existence. Some form of trade advocacy and control group would be very fitting for Stellaris.
The Tleilaxu, meanwhile, are Dune's cloners - think bio-ascension, the "selected lineages" policies, and lots and lots of clones (mostly of Duncan Idaho for some reason).
It's worth noting that the Dune universe has also long since adopted an anti-AI resolution. It's been outlawed and taboo in the Dune universe since humanity's near-extinction at the hand of a machine intelligence (a conflict known by the time period of the first book as Butlerian Jihad), which is why a lot of these interest groups are necessary (in the place of AI, various ways to improve the human capacity were necessary). Something to think about in terms of how interest groups should develop.
Edit: though I haven't seen the film (and so don't know if they let it fall by the wayside), Frank Herbert had a lot to say in the book about ecology through the Fremen's terraforming attempts. Were terraforming made a bit more interesting than an energy sink, pro-terraforming interest groups would also be viable.