Apostasy: No death penalty in Islam
The Quran has guaranteed freedom of conscience for every individual:
"Let there be no compulsion in the religion: Surely the Right Path is clearly distinct from the crooked path." (Al Baqarah, 2:256)
And say: "The truth [has now come] from your Sustainer: let, then, him who wills, believe in it, and let him who wills, reject it." [Part 18:29]
Nevertheless, God condemns apostasy in the Quran – however, there is no proscribed punishment nor any endorsement to punish the apostate in the system (religion) of Islam. As is clearly from the following verses of the Muslim holy scripture:
Do you wish to demand of your messenger something similar to what was demanded of Moses? Whoever exchanges faith for disbelief has strayed far from the right path. [2:108]
If any of you revoke your faith and die as disbelievers, your deeds will come to nothing in this world and the Hereafter, and you will be inhabitants of the Fire, there to remain. [Part of 2:217]
Verily, as for those who are bent on denying the truth after having attained to faith, and then grow [ever more stubborn] in their refusal to acknowledge the truth, their repentance [of other sins] shall not be accepted: for it is they who have truly gone astray. [3:90]
Behold, as for those who come to believe, and then deny the truth, and again come to believe, and again deny the truth, and thereafter grow stubborn in their denial of the truth - God will not forgive them, nor will He guide them in any way. [4:137]
As for anyone who denies God after having once attained to faith-and this, to be sure, does not apply to one who does it under duress, the while his heart remains true to his faith, but [only, to] him who willingly opens up his heart to a denial of the truth-: upon all such [falls] God's condemnation, and tremendous suffering awaits them. [16:106]
At none of these places does the Qur’an mention the punishment of death for such people who change their religion, therefore any ‘secondary sources’ must be interpreted in line with the Quran. However, the Qur’an does mention that such people shall face a terrible punishment in the hereafter but no worldly punishment is mentioned at any of these instances in the Qur’an. Furthermore, the Quran explicitly implies that multiple, sequential apostasies are possible. That would not be possible if the person were executed after the first apostasy.
"Those who believe, then disbelieve, then believe again, then disbelieve, and then increase in their disbelief - Allah will never forgive them nor guide them to the path." [4:137].
The death penalty for apostasy for the sole reason of leaving Islam, and becoming an ‘Ex-Muslim’ is not sanctioned in the Quran – thus, nor in the (religion) system of Islam.
And Allah knows best.
For Younger Readers
God teaches in the Quran, the holy book of Muslims that:
Everyone is free to choose to adopt or leave whichever religion, faith, ideology or way of life
Everyone is responsible and accountable for his/her own choices, in life and before God
There is no death penalty for leaving the religion or system of Islam