Does the Qur'an teach that people who are not Muslims are infidels so it is a crime to change your religion?
These two parts of the question are disjointed. The motive for making apostasy from Islam a capital offense does not derive from the claim that Non-Muslims are infidels (a claim which is less nuanced than the reality). The motive for making apostasy a capital offense is that apostasy is seen as an act of treason against the Muslim community. In the early period of Muhammad and the Rightly-Guided Caliphate, apostasy was a prelude to taking up arms against Muslims. Other reasons have been tacked on since then and prevail in present discourse. For example, Islam is considered by its adherents to be the only truth and those who deny it are setting a bad example that Islam is "just like every other religion" that a person can "try on" and leave at a whim. Also, most people who convert religions tend to slander their prior religion. In order to prevent slander against Islam, ex-Muslims are liable to be killed, silencing them from saying nasty things.
To read more about the punishment for apostasy in Islam, see this Related Question: Why can a Muslim not convert to any other faith?
As we move into the question of what is an infidel, according to Islam, there are three general words used in Arabic to refer to non-believers in an Islamic context. There is Kaafer (often spelled Kafir) which means "denier" or "negator" since they are denying or negating the truth of God. A Kaafer is someone who rejects God in an Islamic context. There is also Mushrik which refers to a polytheist or pagan, i.e. someone who believes in more than one God. Finally, there is Ahl al-Kitaab or Ahl adh-Dhimma which refer to the "People of the Book" or "Protected Peoples", non-Muslim monotheists like Jews and Christians.
The term "infidel" in English is usually used as an analog for Kaafer, not for the other groups, so a person who is not a Muslim is not necessarily an infidel either, he could be a Mushrik or a member of Ahl al-Kitaab. However, the treatment of Mushriks is not terribly different than the treatment of Kaafers and the treatment of the members of Ahl al-Kitaab depends strongly on the particular ruler in place at a given time.
Answer 1 The holy Q'ran does not teach that non Muslims
are infidels. Muslims are taught to treat people of all religions
with respect. However, it is compulsory for Muslims to do what ever
they can do against any people who harm them or prevent them from
There are several reasons why changing one's religion from Islam
to another is a sin in Islam.
--- the following insert is stolen without attribution from Sam
Harris's book The End of Faith
This person lies, all these verses are from the Koran with
teach to kill the infidels, the unbelievers, people of the book,
unbelievers, Christians, and Jews.
Verses from the Koran
Open the Koran, which is perfect in its every syllable, and
simply read it with the eyes of faith. You will see how little
compassion need be wasted on those whom God himself is in the
process of "mocking," "cursing," " shaming," "punishing,"
"scourging," "judging," "burning," "annihilating," "not forgiving,"
and "not reprieving." God, who is infinitely wise, has cursed the
infidels with their doubts. He prolongs their life and prosperity
so that they may continue heaping sin upon sin and all the more
richly deserve the torments that await them beyond the grave. In
this light, the people who died on Sept. 11 were nothing more than
fuel for the eternal fires of God's justice. To convey the
relentlessness with which unbelievers are vilified in the text of
the Koran, I provide a long compilation of quotations below, in
order of their appearance in the text. This is what the Creator of
the universe apparently has on his mind (when he is not fussing
with gravitational constants and atomic weights):
"It is the same whether or not you forewarn them [the
unbelievers], they will have no faith" (2:6).
"God will mock them and keep them long in sin, blundering
blindly along" (2:15).
A fire "whose fuel is men and stones" awaits them
They will be "rewarded with disgrace in this world and with
grievous punishment on the Day of Resurrection" (2:85).
"God's curse be upon the infidels!" (2:89).
"They have incurred God's most inexorable wrath. An
ignominious punishment awaits [them]" (2:90).
"God is the enemy of the unbelievers" (2:98).
"The unbelievers among the People of the Book [Christians and
Jews], and the pagans, resent that any blessing should have been
sent down to you from your Lord" (2:105).
"They shall be held up to shame in this world and sternly
punished in the hereafter" (2:114).
"Those to whom We [God] have given the Book, and who read it
as it ought to be read, truly believe in it; those that deny it
shall assuredly be lost" (2:122).
"[We] shall let them live awhile, and then shall drag them to
the scourge of the Fire. Evil shall be their fate" (2:126).
"The East and the West are God's. He guides whom He will to a
straight path" (2:142).
"Do not say that those slain in the cause of God are dead.
They are alive, but you are not aware of them" (2:154).
"But the infidels who die unbelievers shall incur the curse
of God, the angels, and all men. Under it they shall remain for
ever; their punishment shall not be lightened, nor shall they be
"Slay them wherever you find them. Drive them out of the
places from which they drove you. Idolatry is worse than carnage. .
. . [I]f they attack you put them to the sword. Thus shall the
unbelievers be rewarded: but if they desist, God is forgiving and
merciful. Fight against them until idolatry is no more and God's
religion reigns supreme. But if they desist, fight none except the
"Fighting is obligatory for you, much as you dislike it. But
you may hate a thing although it is good for you, and love a thing
although it is bad for you. God knows, but you know not"
"They will not cease to fight against you until they force
you to renounce your faith-if they are able. But whoever of you
recants and dies an unbeliever, his works shall come to nothing in
this world and in the world to come. Such men shall be the tenants
of Hell, wherein they shall abide forever. Those that have embraced
the Faith, and those that have fled their land and fought for the
cause of God, may hope for God's mercy" (2:217-18).