Here is a long quotation from Wikipedia on the subject of apostasy in Islam.

Apostasy in Islam (Arabic: ارتداد, irtidād or ridda) is commonly defined as the rejection of Islam in word or deed by a person who has been a Muslim.

All five major schools of Islamic jurisprudence agree that a sane male apostate must be executed.[1] A female apostate may be put to death, according to some schools, or imprisoned, according to others. The Islamic laws governing apostasy are derived from the traditions (ahadith). According to Wael Hallaq nothing of the apostasy law are derived from the Qur'an, [2] although the jurist Al-Shafi'i interpreted the Quranic verse [Qur'an 2:217] as providing the main evidence for apostasy being a capital crime in Islam.[3]

Some contemporary Shi'a jurists, scholars, writers and Islamic sects have argued or issued fatwas that either the changing of religion is not punishable or is only punishable under restricted circumstances, but these minority opinions have not found broad acceptance among Islamic scholars.

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Well, I think that this makes it pretty clear that anyone who decides to leave Islam and convert to another religion may well be murdered (or "executed", depending on your viewpoint.)

As for Christians who decide to become Muslims, I have several colleagues (at the school where I am currently teaaching in Doha) who converted to Islam while they were living in England. To the best of my knowledge, no Christians have attacked them or tried to kill them.

Yes, there is an injunction to kill apostates from the Jewish faith in the Book of Deuteronomy. I do not see how this applies to Christians and I cannot find any similar statements in the New Testament. Jesus told his followers to pray for their enemies and to forgive those who persecute them. Christians have not always been keen to follow Jesus' teaching on this point - that's why we had the Crusades - but I think that it would be true to say that the vast majority of Christians today would say that it is wrong to kill someone for their religious beliefs. It seems to me that many Muslims would not agree and would say that apostates from Islam should be killed.