Did Muhammad teach death for apostasy?
The allegation that apostasy is the “ultimate crime” in Islam is false and based off the incorrect assumption that apostasy is a crime that man can punish. Yes, Islam admonishes Muslims to remain Muslims. But what faith encourages its adherents to leave? But even then, Islam is quite liberal. Certain Christians declare eternal hell for those who leave Christianity. Certain Jews consider themselves the chosen people, to the exclusion of all others. Certain Hindus believe in the caste system, forbidding anyone from joining or leaving their caste. Therefore, it is surprising that critics object to the Islamic admonition to not forsake Islam.
In any case, Islam defines the “ultimate crime” against mankind as murder and treason—not apostasy. In fact, murder and treason are the only reasons for which a person may receive capital punishment in Islam . The Qur’an does not allow capital punishment for any other reason. And, as mentioned earlier, even when capital punishment is a possibility, it is by permission, never by commandment.
Critics claim that, “the Koran prescribes death [for apostates],” but not only that Islam does not prescribe death for apostates, the Qur’an was the first religious scripture to categorically declare, “There shall be no compulsion in religion.”  Likewise, the Qur’an repeatedly states that Muslims, including Prophet Muhammad, can only admonish non-Muslims regarding religious matters . The Qur’an addresses disbelief more than 150 times, yet man is never given authority to punish the disbeliever. If Islam sanctioned death for apostasy, why does the Qur’an address—but never sanction—worldly punishment for the apostate who repeatedly believes and disbelieves?  As the majority of these verses were revealed in Medina, not Mecca, critics cannot resort to the “argument” of abrogation of Qur’anic verses.
Prophet Muhammad’s example corroborates the view that no punishment for apostasy exists in Islam. Once, a Bedouin convert to Islam suffered a fever while in Medina. He asked to be released from his pledge three times and was refused three times. Still, he left Medina unharmed. 
If your very own brother, or your son or daughter, or the wife you love, or your closest friend secretly entices you, saying, ‘Let us go and worship other gods’ (gods that neither you nor your fathers have known, gods of the peoples around you, whether near or far, from one end of the land to the other), do not yield to him or listen to him. Show him no pity. Do not spare him or shield him. You must certainly put him to death. Your hand must be the first in putting him to death, and then the hands of all the people. Stone him to death, because he tried to turn you away from the LORD your God, who brought you out of Egypt, out of the land of slavery. 
Arguing that the New Testament sanctions no punishment for apostasy is useless as Jesus Christ stated that nothing of the Old Testament is abrogated . Accordingly, prominent Christian theologians such as St. Thomas Aquinas have endorsed death for apostasy:
Heretics and apostates can be compelled, even physically, to fulfill their promises and hold to do what they once professed … adopting the faith is voluntary, but sticking to it once adopted is obligatory. About heretics there are two things to say. Their sin deserves banishment not only from the church by excommunication but also from the world by death. 
It is remarkable that while critics approve of such teachings, they find fault with the Qur’an for vociferously restricting any worldly punishment for apostasy.
Finally, Islam does not restrict apostasy . Any “punishment” an apostate incurs is a matter between that person and God. The Qur’an, however, is clear: apostasy is not a worldly crime, it is certainly not the “ultimate” crime, apostates are not to be harmed—let alone put to death, and those who choose to leave Islam have every right to do so.
 Qur’an 2:257.
 Qur’an 5:33, “On account of this, We prescribed for the children of Isra’el that whosoever killed a person — unless it be for killing a person or for creating disorder in the land — it shall be as if he had killed all mankind; and whoso gave life to one, it shall be as if he had given life to all mankind. And Our Messengers came to them with clear Signs, yet even after that, many of them commit excesses in the land” (emphasis added).
 Qur’an 2:257.
 Qur’an 4:64; 6:70-71; 10:109; 11:47; 50:46; 88:22-23.
 Qur’an 2:218; 3:21, 73, 91; 4:138; 5:55, 62, 93, 100; 9:3, 66-68, 74; 16:107; 47:26-27; 63:2-7.
 Bukhari [Cairo, n.d.], Vol. 1, Book 3, #28.
 Deuteronomy 13:6-10 (emphasis added).
 Matthew 5:17-18; 23:1-3.
 Summa Theologiae – A Concise Translation by T. McDermott, 339-40.
 Qur’an 4:138; 10:100; 18:30.