I do not know what Islam says about Jews and Christians going to heaven so I asked Google and got the following from
this link where somebody basically asked the same thing:
"Thank you very much for your question.
There is a great difference between the Christian understanding of divine grace and the Muslim understanding of it.
One belief that is generally held by most Christians is that only those who believe that Jesus is the Son of God who underwent the Passion and died for their sins, will go to heaven. No matter that you believe in God and do good works; you will be in hell if you do not accept that Jesus died for you. And even if you lead a horrible life but believe at the same time that Jesus atoned for you in advance, you will be saved and go to heaven.
In contrast to this, the Qur?an very clearly says what means:
*{Those who believe [in the Qur?an], and those who follow the Jewish [scriptures], and the Christians and the Sabians,?any who believe in God and the Last Day, and work righteousness, shall have their reward with their Lord; on them shall be no fear, nor shall they grieve.}* (Al-Baqarah 2:62)
The point of the verse is that Islam does not teach an exclusive doctrine, and it is not meant exclusively for one people. The Jews and Christians hold on to their respective versions of exclusivism, whereas the attitude of Islam is entirely different. Islam existed before the preaching of Muhammad (peace be upon him) on this earth. From the Qur?anic perspective, all those who submitted to God before Muhammad (peace be upon him) were Muslims. Islam or submission to God's will has been and will be the religion for all time and for all peoples.
So it is no surprise that the Qur?an calls Abraham a Muslim. The Qur?an says what means:
*{Abraham was not a Jew nor yet a Christian; but he was true in faith, and bowed his will to God's [which is Islam], and he joined not gods with God.}* (Aal `Imran 3:67)
To call Abraham a Jew or a Christian would be inaccurate, as Judaism and Christianity came after the time of Abraham. Indeed the very names of those religions suggest their beginnings generations after Abraham, while he could very well be called a Muslim, meaning one who submitted to God.
This means that those descendants of Abraham who follow his path are also bound to be in the right. The Qur?an says what means:
*{Without doubt, among men, the nearest of kin to Abraham are those who follow him, as are also this Apostle and those who believe: And God is the Protector of those who have faith.}* (Aal `Imran 3:68)
So what should we say to those who claim that only Jews or Christians will go to heaven? Allah Almighty Himself gives us guidance. The Qur?an says what means:
*{They say: ?Become Jews or Christians if ye would be guided [to salvation].? Say thou: ?Nay! [I would rather] the religion of Abraham the Hanif (the truly-guided), and he joined not gods with God.}* (Al-Baqarah 2:135)
*{Say ye: ?We believe in God, and the revelation given to us, and to Abraham, Isma`il, Isaac, Jacob, and the Tribes, and that given to Moses and Jesus, and that given to [all] prophets from their Lord: we make no difference between one and another of them: and we bow to God [in Islam].}* (Al-Baqarah 2:136)
Thus ,we must understand that all the prophets of God carried the same Message of God and taught the same way to Heaven. And that is Islam.
And Allah knows best.
Thank you and please keep in touch.
Salam."