The main problem of Ibadism is that it's part of a khawrij label (altough that it should be considered as part of what of it is debated, including among Ibadi) and at least outside Arabia, and have more appeal for muladi (converted) than for Arabs as its stressed moral equality of Muslims.
It's especially obvious in al-Ifriqiya and al-Maghrib (possibly al-Andalus as well, tough I don't remember a particularily significant Ibadi presence).
And while it allowed Ibadism (as Khawrij branches in generals) to blossom on marginal communities (socially and/or ethnically and/or socially), it generally prevented them to really reach the cores or elites as a whole.
For medieval North Africa, it basically means a Berber-wank, which is going to be hard to achieve without some orthodox support (as Almoravid beneficied).
People mentioned the Banû Rustam / Rustemids, but the Imamate of Tihert was more about a moral legitimacy on dominance than a strong state, and deprived of a charismatic leader, it tended to go back to the traditional tribal confederation.
Assuming that Ibadi outnumber the Sufris at the time of the Great Berber Revolt of 739/740, and somehow manage to be more successful (basically taking on the whole of al-Ifriqiya and maybe al-Andalus), it might changes things durably.
Not that a Berber Caliphate (Sufri or Ibadi) seems really likely to be anything more than meteoritic to me, due to the structural weakness of their political organisation, but it could give Ibadi a certain legitimity and a strong presence along the coastal line (the true place of power in the region) making the Ibadi communities more than oasis and marginal entities.
An ovbvious PoD would be Abd al-Rahmân ben Rustam being victorious against the wali of al-Misr and managing to keep all al-Ifriqiya, but it doesn't seems really bound to happen : even if he does pulls that, the relative disunity among Arabo-Berbers provide a weakness that Abbasids and their vassals would certainly use, with the possible support of Sufris.
Another PoD may be having Idrissid failing to take on al-Maghrib, allowing tribes as Banû Midrar of Sijilmassa to take on the whole of the region.
Then again we're talking of a mostly tribal entity, at best as cyclical chiefdom.
That said, all of these, if not managing to provide with an Ibadi power in North Africa (which is problematic giving the really tight link between political power and religion in Arabo-Islamic world), gives room for a more widespread Ibadi presence at least for Middle Ages.
Now, the situation is a bit different at the opposite side of the AI world.
Ibadism in Oman and Yemen certainly lacked the ethnic part it had in Africa, but I think it's interesting to point that they still occupied a particular place in the Arabic peninsula, traditionally more open to trade and foreign influence.
As John7755 يوحنا, if you manage to tweak enough things for the Abassids (for the worse) it would certainly give more credence to unheterodox schools both trough legitimacy boost and support from more and more independent-minded elites.
Giving the place of these region on spice trade (
he who controls the spice, controls the universe!).
But that's not the only possibility in Asia, tough : southern Persia, Khwarezm and Sidh can provides room for Ibadi Turks or Turko-Persian entities, would the orthodox caliphates being unable to entierly wheight.
That said, note that Islamic branches and schools were quite porous to each other until the end of medieval era (even if you do have periods of dogmatisation of these, critically with Fatimid rise) : a more successful Ibadi presence in Arabo-Islamic world could mean that some of their beliefs and principles being adopted (after modification) by mainstream Islamic teachings, thus making them either less distinguishable, or less successful.