Does Islam prescribe death for the Muslim who converts to another religion?
Those who turn their back on Islam are to be put to death. This is confirmed by the words and deeds of Muhammad. There is no such thing as freedom of belief in Islam.
Qur'an (9:11-12) - "But if they repent and establish worship and pay the poor-due, then are they your brethren in religion. We detail Our revelations for a people who have knowledge. And if they break their pledges after their treaty (hath been made with you) and assail your religion, then fight the heads of disbelief - Lo! they have no binding oaths - in order that they may desist."
This verse is speaking of infidels (i.e.. "slay the infidels wherever you find them" 9:5) who obviously became Muslim to escape the sword, but the Hadith make no distinction of how a Muslim came to be a Muslim. Apostasy is always punished by death.
Other verses that seem to support the many Hadith demanding death for apostates are Qur'an verses 2:217, 9:73-74, 88:21, 5:54, and 9:66.
Advocates for killing apostates have pointed out that the supporting hadith are reliable and thus qualify as law according to verse 4:80 - "Whoso obeyeth the Messenger obeyeth Allah."
From the Hadith:
The reason why executing apostates has always been well-ensconced in Islamic law is that there is an indisputable record of Muhammad and his companions doing exactly that.
Bukhari (52:260) - "...The Prophet said, 'If somebody (a Muslim) discards his religion, kill him.' "
Bukhari (83:37) - "Allah's Apostle never killed anyone except in one of the following three situations: (1) A person who killed somebody unjustly, was killed (in Qisas,) (2) a married person who committed illegal sexual intercourse and (3) a man who fought against Allah and His Apostle and deserted Islam and became an apostate."
Bukhari (84:57) - "[In the words of] Allah's Apostle, 'Whoever changed his Islamic religion, then kill him.'"
Bukhari (89:271) - A man who embraces Islam, then reverts to Judaism is to be killed according to "the verdict of Allah and his apostle."
Bukhari (84:58) - "There was a fettered man beside Abu Muisa. Mu'adh asked, 'Who is this (man)?' Abu Muisa said, 'He was a Jew and became a Muslim and then reverted back to Judaism.' Then Abu Muisa requested Mu'adh to sit down but Mu'adh said, 'I will not sit down till he has been killed. This is the judgement of Allah and His Apostle (for such cases) and repeated it thrice.' Then Abu Musa ordered that the man be killed, and he was killed. Abu Musa added, 'Then we discussed the night prayers'"
Bukhari (84:64-65) - "Allah's Apostle: 'During the last days there will appear some young foolish people who will say the best words but their faith will not go beyond their throats (i.e. they will have no faith) and will go out from (leave) their religion as an arrow goes out of the game. So, wherever you find them, kill them, for whoever kills them shall have reward on the Day of Resurrection.'"
Reliance of the Traveller (Islamic Law) o8.1 - "When a person who has reached puberty and is sane voluntarily apostatizes from Islam, he deserves to be killed." --- (o8.4 affirms that there is no penalty for killing an apostate.)
Muslims are commanded to fight unbelievers until they are either dead, converted to Islam, or in a permanent state of subjugation under Muslim domination. Allowing people of other faiths to live and worship independently of Islamic rule is not an option.
Qur'an (9:29) - "Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Messenger, nor acknowledge the religion of Truth, (even if they are) of the People of the Book, until they pay the Jizya with willing submission, and feel themselves subdued."
Suras 9 and 5 are the last "revelations" that Muhammad handed down.
Qur'an (9:5) "But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, and seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practice regular charity, then open the way for them..."
Qur'an (9:11) - (Continued from above) "But if they repent and establish worship and pay the poor-due, then are they your brethren in religion"
- This confirms that Muhammad is speaking of conversion to Islam.
Qur'an (2:193) - "And fight them until persecution is no more, and religion be only for Allah. But if they desist, then let there be no hostility except against wrong-doers." The key phrase is to fight until "religion be only for Allah."