Who are the Ahlus-Sunnah Wal-Jamaa’ah? If the Ashaa’irah and Maatureediyyah are not from the Ahlus-Sunnah Wal-Jamaa’ah, then who is?
If you classify them under the Islamic sects, you are dubbing them disbelievers and the possibility of their admittance into Hell.

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

Ahlus-Sunnah Wal-Jamaa’ah are those who follow the Prophet, sallallaahu ‘alayhi wa sallam, the Companions, the successors of the Companions, and those who follow them precisely in speech, belief and practice. They have no other name but Ahlus-Sunnah Wal-Jamaa‘ah. Their principles include belief in Allaah The Almighty, His Angels, His Books, His Messengers, the Last Day and destiny -- whether good or evil. They also affirm whatever Allaah The Almighty established for Himself and whatever the Prophet, sallallaahu ‘alayhi wa sallam, established for Allaah The Almighty and reject whatever Allaah The Almighty and the Prophet, sallallaahu ‘alayhi wa sallam, rejected as not attributed to Allaah The Almighty. They believe that ’Eemaan (faith) consists of speech, belief and practice, and that it is liable to increase or decrease. They do not accuse Muslims of disbelief for committing any act of disobedience or major sin as the Khawaarij (a deviant sect) do.

A further characteristic of Ahlus-Sunnah Wal-Jamaa‘ah is their unblemished view of the Companions, whom Allaah The Almighty described as (what means): {And [there is a share for] those who came after them, saying, "Our Lord, forgive us and our brothers who preceded us in faith and put not in our hearts [any] resentment toward those who have believed. Our Lord, indeed You are Kind and Merciful."}[Quran 59:10]

Ahlus-Sunnah also follow the traditions of the Prophet, sallallaahu ‘alayhi wa sallam, both its outward and inward aspects, and they follow the example of the first of the faithful among Muhaajiroon (emigrants) and Ansaar (their helpers in Madeenah).  

Additionally, Ahlus-Sunnah enjoin the good and forbid evil according to the Sharee‘ah and affirm the need to observe Hajj, Fridays and ’Eeds with their rulers, whether the rulers are righteous or not. Ahlus-Sunnah are those who follow the pure, unblemished Islam.

The Ashaa’irah, on the other hand, trace back their origins to Imaam Abu Al-Hasan Al-Ash‘ari who experienced three stages of thought according to Ibn Katheer and Az-Zubaydi and others.

The first stage marked his adoption of the Mu‘tazili thought; the second witnessed his following of Ibn Kullaab; and the third marked his following of Ahlus-Sunnah, led by Imaam Ahmad ibn Hanbal . Abu Al-Hasan Al-Ash‘ari declared this last stance in his books. Anyone who follows him in the third stage in fact conforms to Ahlus-Sunnah in most of their beliefs, and anyone following him in the second stage contradicts Imaam Al-Ash’ari himself as well as Ahlus-Sunnah in many of their beliefs. 

The Maatureediyyah are traced back to Abu Mansoor Al-Maatureedi who died in 333 AH. They have principles that are contradictory to Ahlus-Sunnah. Their disagreement with the Ashaa’irah is confined to a few issues -- mentioned by some as 13 in number.  The disagreement on some of these issues is in terms of wording only.

With regard to Takfeer (considering another person who is outwardly Muslim as a disbeliever), then this is a Sharee‘ah ruling. Therefore, a disbeliever is the person who is considered a disbeliever in the sight of Allaah and the Prophet, sallallaahu ‘alayhi wa sallam. No one is entitled to practice Takfeer with his own criteria as that is exclusive to Allaah The Almighty.

Shaykh Al-Islam Ibn Taymiyyah said that no one may stigmatize any Muslim with disbelief, even if the person has committed huge errors, until the perpetrator has been educated beyond excuse of ignorance and doubt, and the right way has been shown to him. Anyone who is a Muslim cannot be considered otherwise based only on doubts. A Muslim cannot be considered a disbeliever for committing a mere mistake or slip, but rather only for something, supported by evidence, which is an act of major disbelief leading to apostasy. Prior to making any accusation of Takfeer, certain conditions must be met: the accused person must have committed disbelief by word, deed or belief; and the impediments of Takfeer must be absent, such as ignorance, misunderstanding, doubts, a lack of education beyond the excuse of ignorance etc.

And Allaah Knows best.