Who is the accountable person who must enter Islam, and follow its teachings?

Praise be to Allah.

Firstly:

The accountable person who is obliged to enter Islam and follow its teachings is the one who is an adult of sound mind, whom the call of Islam reached and proof was established against him.

Abu Dawood (4403) and at-Tirmidhi (1423) narrated from ‘Ali (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “The Pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty and from the insane person until he comes to his senses.”

It says in al-Mawsoo‘ah al-Fiqhiyyah (4/36):

The majority of fuqaha’ are of the view that the criterion of accountability is reaching puberty, not reaching the age of discernment, and that the child who has reached the age of discernment is not obliged to do any religious duties, and will not be punished in the hereafter for failing to do any duty or for doing any prohibited action, because the Prophet (blessings and peace of Allah be upon him) said: “The Pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty and from the insane person until he comes to his senses.” End quote.

In the same book (30/264) it says:

The fuqaha’ are unanimously agreed that sanity is one of the conditions of accountability, so no act of worship – such as prayer, fasting, Hajj, jihad and so on – is obligatory upon anyone who is not of sound mind, such as one who is insane, even if he is an adult Muslim. End quote.

Shaykh al-Islam Ibn Taymiyyah (may Allah have mercy on him) said:

The Qur’an and Sunnah indicate that Allah does not punish anyone until after the message reaches him. Those whom the message did not reach at all will not be punished at all. Those whom it reached, but it was lacking in some details, will not be punished except if they deny issues concerning which proof was established against them. For example, Allah, may He be exalted, says (interpretation of the meaning):

“so that mankind will have no argument against Allah after the messengers”

[an-Nisa’ 4:165]

“ ‘O company of jinn and mankind, did there not come to you messengers from among you, relating to you My verses and warning you of the meeting of this Day of yours?’ They will say, ‘We bear witness against ourselves’; and the worldly life had deluded them, and they will bear witness against themselves that they were disbelievers”

[al-An‘aam 6:130]

“But did We not grant you life enough for whoever would remember therein to remember, and the warner had come to you?”

[Faatir 35:37]

“And never would We punish until We sent a messenger”

[al-Isra’ 17:15].

End quote from Majmoo‘ al-Fataawa (12/493).

For more information, please see the answer to question no. 239026.

Secondly:

Uttering the Shahaadatayn (the twin declaration of faith) is a condition of entering Islam, for the one who is able to utter these words.

Shaykh al-Islam Ibn Taymiyyah (may Allah have mercy on him) said:

As for the Shahaadatayn, if a person does not utter these words when he is able to do so, then he is a disbeliever according to the consensus of the Muslims, and he is a disbeliever both inwardly and outwardly, according to the early generations of the ummah, its imams (leading scholars) and the majority of its scholars.

End quote from Majmoo‘ al-Fataawa (7/609)

See also the answer to question no. 655

And Allah knows best.