It's an interesting question, because Ibadism itself has quite the eventful history. Early and Medieval Omani history is very pooly documented, so some of this is a little general and hand-wavey (especially the earlier dates). It's a long story, so I provided a summary at the end. But first, a little bit of the geography (it's important, I promise).

Oman is a bit of a patchwork state, similar to Saudi Arabia, which is historically a source of regional and social tension. It can generally be divided into the coastal and inland regions. The coastal regions include the trading hub of Muscat and the agricultural areas of the Southern Coast, and is historically where most of the traders, merchants, sailors, and foreigners lived. Being such a wealthy region, it was occasionally invaded and ruled by various foreign powers as well. All this combined to give it a cosmopolitan, tolerant culture. Different ruling groups had different religious leanings, helping to establish minorities of several religions and denominations.

The inland region is traditionally home to nomadic tribesmen, similar to those in Saudi Arabia. Bordering on the Rub Al-Khali, There's very little in terms of resources here, and it was occasionally used as a place of exile for political and religious dissidents.

Now, Ibadism is considered either an offshoot of the Kharijite movement, or a development from a predecessor group that later gave rise to both, but there is a connection between the two, with Ibadi groups occasionally being sponsored by the Caliphates as moderate allies against the extremist Kharijites. The Ibadi movement started in Medina but grew primarily in Basra, and opposed the Caliph Uthman. Out of political and religious favor for this, Ibadi agitators were frequently exiled to the interior of Oman. On the other side of the Rub Al-Khali, this effectively isolated them, as they had little influence amongst the ruling powers of Muscat or northwestern Yemen. On the other hand, this isolation allowed the Ibadi scholars to come to positions of power within the various nomadic tribes, who soon converted to Ibadism. These tribes established Imamates, and elected Imams from amongst the tribal leaders. The Imamates waxed and waned in power and significance through the years, and were occasionally in conflict with the more secular sultans of Muscat. Slowly however, Ibadism made it's way into the more populous coastal areas as well.

At about the same time as the Ibadis were growing in the interior of Oman, Uthman's tribe established the Umayyad Caliphate after his murder, and various Ibadis moved to the Hijaz and attempted a revolt. They were eventually driven from the Hijaz to Sanaa, and then into eastern Yemen (Hadramawt), before a peace deal was signed to allow the Umayyads to concentrate their forces elsewhere. Various Ibadi groups now controlled everything from the southern Yemeni coast to Oman. They were still technically subjects of the Caliphs, but were largely autonomous. Occasional forays into the area were undertaken by different powers, including Persia and the Seljuqs, interspersed with native Imamates and Sultanates. As mentioned before, the outside powers largely ignored the poor interior.

Eventually, in the early 1500s, the Portuguese invaded and captured Muscat from the native Nabhani dynasty. They managed to extend their holdings up and down the eastern coast, and held power for nearly 150 years, with occasional periods of Ottoman control. The Nabhanis were unable to retake any of their previous holdings, and were supplanted in turn by the Yarubid dynasty. The Yarubids were Ibadi tribesmen from the interior who managed to unify the various tribes for the purposes of expelling the Portuguese, which they managed to do - so successfully in fact, that they went on the offensive by beefing up the navy and capturing the island of Zanzibar, the only other predominantly Ibadi Muslim area in the world. They also intermittently controlled other areas of Portuguese East Africa (notably Mombasa), and attacked Portuguese holdings in India, giving them a reputation (and appetite) for piracy. The Yarubids are important for changing the historically elected position of Imam into a hereditary title. Previous dynasties existed but had ruled under different titles - frequently Sultan.

Eventually, in the early- and mid-18th century, a succession crisis destabilized the region, allowing the Persians to once again occupy parts of the Muscat coast. The Persian rule was immediately unpopular, and another Ibadi tribesman named Ahmad bin Said al-Busaidi, who had become governor of the coastal city of Sohar, revolted. After fighting against the Persians and later Yarubid Imams, he managed to solidify his power and was himself elected Imam in 1749. He established the Ibadi Al Said dynasty, which continues to this day, in Qaboos bin Said al Said. It's interesting to note, however, that the Al Said dynasty quickly lost the title of Imam, becoming instead Sultan (or sometimes Sayyid). The Imamate continued, frequently in conflict with the Sultans. Thanks to outside (usually British) aid, they managed to maintain control and reconquer the interior.

TL;DR - The isolated and poor interior of Oman, ignored by almost everyone, became Ibadi after scholars migrated or were exiled there and were elected to positions of power in the native tribes. Fast forward a thousand years, and these tribes were unified by the Al Said dynasty, and established their power over the coastal regions, driving out the incumbent foreign powers. Also Zanzibar and Mombasa.

Sources: The New Cambridge History of Islam, edited by Francis Robinson (I don't remember which volume, unfortunately, but I can check if needed), and History of the imams and seyyids of Oman: A.D. 661-1856 by Salil ibn-Raziq and translated by Hamid ibn Muhammad ibn Ruzayq