Who are the Khawarij to the Ibadhis?
To the Ibadhis, to go out out from the religion of Islam has nothing directly to do with political rebellion, be it legal or illegal rebellion. It is based soley upon the rejection of the fixed Shariah laws practiced by the Prophet Mohamed sallalahu alahi wa salaam, or committing acts against the set of prescribed binding laws for religious practice, like the prolonged abandonment of prayer or acts of worship for others than Allah alone. Thus they do no consider their practice of Islam to be out of the confines of Islam. If they had used the definition of rebelling against a right (or even wrong) leader, then they would have been Khawarij and labelled Uthman's killers, Talhah & al-Zubair, and Muawiyah as such.
Logical definition, which gets rid of the necessity of having to define what a "right leader" is in order to understand the term Khawarij, unlike my Sunni sources.
So do the Ibadhi consider anyone to be Khawarij?
Yes, they consider the Azariqah Sect and its supporters to be Khawarij because Nafi Al-Azraq made the mistake of deriving a religious ruling from a single peice of [misunderstood by him when taken out of context] Islamic evidence, rather than the volume of evidence in sunnah of the Prophet Mohamed sallalahu alahi wa salaam's lifetime.
The Ibadhi believe that the Azariqah sect has gone out of the religion because they have rejected the shariah that guards that a Muslim's personage is safe unless they should apostate. [Osama Bin Laden falls into this category for example, as he believes killing innocent civilians and even Muslims to be okay by rationalization of out-of-context Qu'ran quotes not within the example of the Shariah laws set out by Rasoolulah Mohamed].
In such an example of saying that the Azariqah are khawarij, how is that rationalized?
The Azariqah believe that if a Muslim commits a major or minor sin, then it is lawful to shed their blood, capture their pocessions, and enslave their women and children, as it is quoted in the Qu'ran in Surah al-An'am, ayah 121: "And if you obey them you verily are surely polytheists [ie disbelievers, apostates]". Thus the Azariqah believe that Muslim believers [and innocent civilians] became/become apostates/polytheists when they committed/commit sins, even very minor ones.
The Ibadhi (and Sunni me, and all the Shia ladies that I know personally know) do not believe such rationalizing is correct. Firstly, the ayah is in context of telling us to eat halal meat, and that Allah compares those who do not follow His clearly prescribed conditions to the disbelievers. Secondly, and most importantly, there were Muslims alive during the Prophet Mohamed's [sallalalhu alahi wa salaam] time who used to commit sins, even major ones, but they were not subject to the laws for militant disbelievers who attacked the Muslims, or of Muslim apostates. Thus such a ruling is cleaaaaaaaaaarly imcompatible with the Shariah itself, and is a rejection of the foundations of the Shariah.
If one is to follow the Azariqah school of thought, all manner of horrors and attrocities can be committed upon the Ummah [Muslim nation and others friendly to us]. Jealous of your neighbor and want his lands? Find a small fault in him and then murder him, it's okay. That woman from your village who won't marry you? Fine. Point out that headscarf doesn't go quite enough over her breasts, and take her as your slave. She's not a Muslim afterall then is she? Or we could go with Osama. Any Muslim whose not fighting America deserves to die because they are personally responsible for their government's killing of Palestinians. Scary, the result of such a rejection of the sunnah, and shariah, isn't it?
To the Ibadhi the Azariqah are not Khawarij because they seceded from Ali R.A after the arbitration, or because they rebelled against the Umayyads. They are Khawarij because they misinterpreted verses from the Qu'ran, which in turn led them to commit acts of wickedness, and to invalidate laws. To the Ibadhi, rebellion against a Caliph or an Imam does not result in the renuncification of Islam, even if those who do so are deemed disobedient, sinful, or aggressors from within the contexts of Shariah law.
To the Ibadhi Sect's school of thought, Muslims only become Khawarij through their deeds [acts of apostasy as defined by Allah's & His Messenger] and doctrines [that reject the Shariah and thus the Messenger and the Quran], but not rebellion in itself, or sins that did not lead to apostasy.