Within the methodology of the Khawārij is the takfīr on Muslims (declaring them to be non-Muslims) without just cause. Their methodology involves the killing of the Muslims and killing of the unbelievers who live within the land of the Muslims guaranteed in safety. Furthermore, they try to justify the killing of women, children and also suicide bomibng.
The Khawārij are a people that if you were to compare your prayer to their prayer you would find yours to be less, the same goes for fasting and recitation of the Qurʾān, despite all of this, the Prophet (صلى الله عليه وسلم) said about them: “Your recitation of the Qurʾān is nothing compared to their recitation. Your prayer is nothing compared to their prayer. And your fasting is nothing compared to their fasting. They will recite the Qurʾān thinking that is (a proof) for them, when in fact it is (a proof) against them. Their prayer will not go beyond their throats. They will shoot out from Islām just as the arrow shoots out from the hunted prey." [Ṣaḥīḥ Muslim: Book of Zakāt (no. 1066)].
The Prophet (صلى الله عليه وسلم) also said: "If I would reach them (i.e. their time), I would surely kill them with the slaughter the people of Thamūd experienced.” [ Ṣaḥīḥ Muslim: Book of Zakāt (no. 1066)].
The Prophet (صلى الله عليه وسلم) describes them as "the dogs of the hell fire". The Shaykh mentions, Allāh the Most High says:
وَمَا أُمِرُوا إِلَّا لِيَعْبُدُوا اللَّـهَ مُخْلِصِينَ لَهُ الدِّينَ حُنَفَاءَ وَيُقِيمُوا الصَّلَاةَ وَيُؤْتُوا الزَّكَاةَ ۚ وَذَٰلِكَ دِينُ الْقَيِّمَةِ
"And they were commanded not, but that they should worship Allāh, and worship none but Him Alone (abstaining from ascriibng partners to Him), and perform al-Ṣalāt (Iqāmat al-Ṣalāt) and give Zakāt: and that is the right religion."
Lastly, there was a question asked to the Shaykh:
[Q]: What is the ruling for those people who make excuses for the Khawārij, those who kill the Muslims and cause corruption to people's property and they kill the people?
[A]: The people that find excuses for them, make excuses for them, give them excuses, they are just like them! They are just the same as them! The ones who make the excuses for them are just like them! They are just the same as them! The ones who make the excuses for them are just like them people who do those things! They are misguided, they are people astray, just the same as them!