Is it permissible for ordinary people to label as a kaafir one who reviles Islam, without referring to the scholars concerning that?

Firstly: 

There is no doubt that reviling Allah, may He be exalted – Allah forbid – or reviling His Messenger or His religion – Allah forbid – comes under the heading of disbelief in Allah the Almighty. The one who does that has committed major kufr that puts one beyond the pale of Islam. If he dies in that state without having repented from it, then he will be one of the people of Hell who will abide therein for all eternity. 

Shaykh Ibn Baaz (may Allah have mercy on him) said: 

The scholars are unanimously and definitively agreed that if a Muslim reviles Islam, or criticises it, or he reviles the Messenger (blessings and peace of Allah be upon him), or criticises or mocks him, then he is an apostate and a kaafir and it is permissible to sentence him to death and seize his wealth.

End quote from Fataawa Noor ‘ala ad-Darb by Ibn Baaz, p. 139 

Shaykh Ibn Jibreen (may Allah have mercy on him) was asked:

What is the ruling on one who reviles Allah and His Religion? What is the expiation for that? Please note that the man concerned is married; does his wife become haraam for him or is she divorced? 

He replied:

There is no doubt that this is apostasy from Islam and disbelief in Allah for which the person who does it deserves to be sentenced to death unless he repents; his wife is divorced from him and his ties of kinship with his relatives are severed, so he does not inherit from them and they do not inherit from him. But if he repents, regrets it, prays for forgiveness and acknowledges his mistake, Allah will accept his repentance and he can take his wife back if her ‘iddah has not ended; if it has ended then it is up to her, and it is not permissible for him to take her back except with her consent.

End quote from Fataawa Islamiyyah, 3/533 

Secondly: 

If a person hears someone clearly reviling Allah, or shar‘i proof is established to that effect, then there is nothing wrong with him believing that this person is a kaafir. This is the most abhorrent and serious kind of reviling, and no one does that except one who has gone far astray and has no respect for Allah, may He be glorified and exalted, or one who has lost his mind and does not know what he is saying. 

This kind of reviling is not one of the obscure issues that need a ruling from the scholars or need to be subjected to examination; rather it is something very clear and obvious that can be recognised by ignorant and knowledgeable alike, and old and young will be disgusted by it. 

But at the same time it is essential to bear in mind the shar‘i purpose behind denouncing that and regarding it as repugnant, which is to remove and ward off that evil and to strive to make the one who said it repent and come back to his Lord, even if he has apostatised and gone beyond the pale of Islam. Asking the apostate to repent is something that is well known and well established. So efforts should be made to exhort him in a manner that is appropriate to his situation, explaining the abhorrent nature of what he has done and to discuss with him the shar‘i way that is appropriate to his situation. 

The scholars of the Standing Committee said: 

Reviling Islam – Allah forbid – is kufr according to the texts and scholarly consensus. Allah, may He be exalted, said (interpretation of the meaning):

“Was it at Allah, and His Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.) and His Messenger (SAW) that you were mocking?

Make no excuse; you have disbelieved after you had believed”

[at-Tawbah 9:65].

And there are other similar texts. 

It is essential to advise him and denounce him for that; if he responds, praise be to Allah, otherwise it is not permissible to initiate the greeting of salaam with one who has reviled Islam, or to return his greeting if he initiates the greeting; it is not permissible to accept his invitation and he must be shunned completely until he repents or until the ruling of Allah, which is to be sentenced to death, is carried out on him by the authorities, because the Prophet (blessings and peace of Allah be upon him) said: “Whoever changes his religion, execute him.” Narrated by al-Bukhaari in his Saheeh, 3017.

End quote from Fataawa al-Lajnah ad-Daa’imah, 2/12 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:

If a person repents from any sin, even if that was reviling Islam, his repentance will be accepted, if he fulfils the conditions that we have mentioned. However it should be noted that a word may constitute kufr or apostasy, but the one who utters it does not (necessarily) become a kaafir thereby, because of the presence of some factor that prevents him being labelled as a kaafir. In the case of this man who said that he reviled Islam in a moment of anger, we say to him: If your anger was so severe that you did not know what you were saying, and you did not know whether you were in the sky or on the ground, and you said something without thinking and not knowing what you were saying, there is no ruling that is applicable to these words and you are not to be labelled an apostate, because this is something that was said involuntarily and without thinking, and if anything is said involuntarily and without meaning to, Allah, may He be glorified and exalted, will not bring one to account for it. Allah, may He be exalted, says concerning vows (interpretation of the meaning): “Allah will not call you to account for that which is unintentional in your oaths, but He will call you to account for that which your hearts have earned” [al-Baqarah 2:225].

End quote from Fataawa Noor ‘ala ad-Darb, 24/2 

For more information on the guidelines on labelling anyone as a kaafir, please see the answer to question no. 85102 

And Allah knows best.