This is a fundamentally important question in Islam. If the People of the Book are indeed believers, then Islam is not necessary to avoid eternal torment in hell. However, if the People of the Book are disbelievers, then Allah has a lot to answer for...namely why did he allow for so many people to be led astray by books they themselves did not corrupt? A typical Islamic response would be: "It's a test." But if that's the case, why would any omniscient (all-knowing) being require a test to know the hearts of men? And why create an eternal torture chamber to punish those humans who failed the test when he knew they were going to fail before he even created them? Allah is either a sadist or he is not omniscient.
Will Jews and Christians be saved from hell?
—Those who believe (in the Qur'an), and those who follow the Jewish (scriptures), and the Christians and the Sabians,- any who believe in Allah and the Last Day, and work righteousness, shall have their reward with their Lord; on them shall be no fear, nor shall they grieve.
—Those who believe (in the Qur'an), those who follow the Jewish (scriptures), and the Sabians and the Christians,- any who believe in Allah and the Last Day, and work righteousness,- on them shall be no fear, nor shall they grieve.
— Truly, the religion with Allah is Islam. Those who were given the Scripture (Jews and Christians) did not differ except, out of mutual jealousy, after knowledge had come to them. And whoever disbelieves in the Ayah (proofs, evidences, verses, signs, revelations, etc.) of Allah, then surely, Allah is Swift in calling to account.
—If anyone desires a religion other than Islam (submission to Allah), never will it be accepted of him; and in the Hereafter he will be in the ranks of those who have lost (All spiritual good).
Are Jews and Christians going to be punished in the place of sinful Muslims?
According to the Qur'an, people can carry the burdens of other people's sins
—Let them bear, on the Day of Judgment, their own burdens in full, and also (something) of the burdens of those without knowledge, whom they misled. Alas, how grievous the burdens they will bear!
—They will bear their own burdens, and (other) burdens along with their own, and on the Day of Judgments they will be called to account for their falsehoods.
Jews and Christians will be punished in the place of Muslims
—Abu Musa' reported that Allah's Messenger (may peace be upon him) said: When it will be the Day of Resurrection Allah would deliver to every Muslim a Jew or a Christian and say: That is your rescue from Hell-Fire.
—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).
—Abu Burda reported Allah's Messenger (may peace be upon him) as saying: There would come people amongst the Muslims on the Day of Resurrection with as heavy sins as a mountain, and Allah would forgive them and He would place in their stead the Jews and the Christians. (As far as I think), Abu Raub said: I do not know as to who is in doubt. Abu Burda said: I narrated it to 'Umar b. 'Abd al-'Aziz, whereupon he said: Was it your father who narrated it to you from Allah's Apostle (may peace be upon him)? I said: Yes.
Acording to the Qur'an, people cannot carry the burdens of other people's sins--Doh!
—Who receiveth guidance, receiveth it for his own benefit: who goeth astray doth so to his own loss: No bearer of burdens can bear the burden of another: nor would We visit with Our Wrath until We had sent an messenger (to give warning).
—Say: "Shall I seek for (my) Cherisher other than Allah, when He is the Cherisher of all things (that exist)? Every soul draws the meed of its acts on none but itself: no bearer of burdens can bear of burdens can bear the burden of another. Your goal in the end is towards Allah: He will tell you the truth of the things wherein ye disputed."
—Namely, that no bearer of burdens can bear the burden of another
—And the Unbelievers say to those who believe: "Follow our path, and we will bear (the consequences) of your faults." Never in the least will they bear their faults: in fact they are liars!
Should Jews and Christians follow their scriptures?
Jews should follow the Torah (nevermind that the Qur'an contradicts the Torah)
—How come they unto thee for judgment when they have the Torah, wherein Allah hath delivered judgment (for them)? Yet even after that they turn away. Such (folk) are not believers.
Christians should follow the Gospel (nevermind that the Qur'an contradicts the Gospel)
—And in their footsteps We sent Jesus the son of Mary, confirming the Law that had come before him: We sent him the Gospel: therein was guidance and light, and confirmation of the Law that had come before him: a guidance and an admonition to those who fear Allah. Let the people of the Gospel judge by what Allah hath revealed therein. If any do fail to judge by (the light of) what Allah hath revealed, they are (no better than) those who rebel.
Allah has given different scriptures for different groups of people to follow
—To thee We sent the Scripture in truth, confirming the scripture that came before it, and guarding it in safety: so judge between them by what Allah hath revealed, and follow not their vain desires, diverging from the Truth that hath come to thee. To each among you have we prescribed a law and an open way. If Allah had so willed, He would have made you a single people, but (His plan is) to test you in what He hath given you: so strive as in a race in all virtues. The goal of you all is to Allah; it is He that will show you the truth of the matters in which ye dispute;
The Qur'an supposedly confirms the previously revealed scriptures (i.e. the Torah and Injil)
—O Children of Israel! call to mind the (special) favour which I bestowed upon you, and fulfil your covenant with Me as I fulfil My Covenant with you, and fear none but Me. And believe in what I reveal, confirming the revelation which is with you, and be not the first to reject Faith therein, nor sell My Signs for a small price; and fear Me, and Me alone.
—And when there comes to them a Book from Allah, confirming what is with them,- although from of old they had prayed for victory against those without Faith,- when there comes to them that which they (should) have recognised, they refuse to believe in it but the curse of Allah is on those without Faith.
A Christian or Jew can be a disbeliever despite faithful adherence to their scriptures
—Those who reject (Truth), among the People of the Book and among the Polytheists, were not going to depart (from their ways) until there should come to them Clear Evidence,- An messenger from Allah, rehearsing scriptures kept pure and holy: Wherein are laws (or decrees) right and straight. Nor did the People of the Book make schisms, until after there came to them Clear Evidence. And they have been commanded no more than this: To worship Allah, offering Him sincere devotion, being true (in faith); to establish regular prayer; and to practise regular charity; and that is the Religion Right and Straight. Those who reject (Truth), among the People of the Book and among the Polytheists, will be in Hell-Fire, to dwell therein (for aye). They are the worst of creatures.
According to the Gospel, Jesus is the Son of God. According to the Qur'an, he is not.
—Then the high priest stood up and said to Jesus, "Are you not going to answer? What is this testimony that these men are bringing against you?" But Jesus remained silent.
The high priest said to him, "I charge you under oath by the living God: Tell us if you are the Christ, the Son of God.""Yes, it is as you say," Jesus replied. "But I say to all of you: In the future you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven."
—The Jews call 'Uzair a son of Allah, and the Christians call Christ the son of Allah. That is a saying from their mouth; (in this) they but imitate what the unbelievers of old used to say. Allah's curse be on them: how they are deluded away from the Truth!
What it all comes down to is belief in Muhammad...not Allah
—It is narrated on the authority of Abu Huraira that the Messenger of Allah (may peace be upon him) observed: By Him in Whose hand is the life of Muhammad, he who amongst the community of Jews or Christians hears about me, but does not affirm his belief in that with which I have been sent and dies in this state (of disbelief), he shall be but one of the denizens of Hell-Fire.