Yet, this is not what Islam teaches.
Allah will place the sins of the Muslims on the Christians and Jews.
Abu Burda reported on the authority of his father that Allah’s Apostle (may peace be upon him) said: No Muslim would die but Allah would admit IN HIS STEAD a Jew or a Christian in Hell-Fire. ‘Umar b. Abd al-‘Aziz took an oath: By One besides Whom there is no god but He, thrice that his father had narrated that to him from Allah’s Messenger (may peace be upon him). (Sahih Muslim, Book 037, Number 6666)
[Also, since Allah leads astray who he wills, there is nothing that dawah (islamic preaching) can do to change what Allah has already done. There is also nowhere in the Kuran directing Muslims to dawah in fact, it says not to dispute with Christians but to say that they believe in what (the revelation) was sent down to them.
The Kuran tells them repeatedly to believe in the books, angels, prophets and the last day. I have yet to have a Muslim that can follow these commands without saying, either the books are lost or corrupted. Yet its a command till the day of resurrection.