In further explaination of this verse: “Those who believe (in the Qur’an) and those who follow the Jewish (Scriptures), and the Christians and the Sabians, and 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” [Qur'an 2:62].
I offer this in order to leave no room for misunderstanding-
And whoever desires a religion other than Islam, it shall not be accepted from him, and in the hereafter he shall be one of the losers. [3:85].
This verse according to most scholars abrogates the previous verse since the first verse listed is referring to the people before Islam was revealed. The key here is a firm belief in monotheism which Jews and Christians originally believed in. This is unto itself a very lengthy discussion and one I am willing to elaborate on for the truly interested people who want to know the truth with the intention of accepting it.
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 [5:48].