[Islam is considered the latest articulation of the religion that God has articulated over and over again in different places and different times to different peoples.
That means different messengers have been sent in the past who have established different religions. As long as such a religion affirms the oneness of God and the importance of ethical relations among people then it is a religion that God accepts.
The following verses from the Quran give glimpses of this interfaith/multi-faith understanding.
The following translations of the Quran are adapted from those made by M. M. Pickthall. His translation is a bit dated, but it still carries a certain charm.]
There is no compulsion in religion. The right direction is henceforth distinct from error. And he who rejecteth false deities and believeth in God hath grasped a firm handhold which will never break. God is Hearer, Knower.
Verily We sent messengers before thee, among them those of whom We have told thee, and some of whom We have not told thee; and it was not given to any messenger that he should bring a portent save by God’s leave, but when God’s commandment cometh (the cause) is judged aright, and the followers of vanity will then be lost.
Lo! We did reveal the Torah, wherein is guidance and a light, by which the prophets who surrendered (unto God) judged the Jews, and the rabbis and the priests (judged) by such of God’s Scripture as they were bidden to observe, and thereunto were they witnesses. So fear not mankind, but fear Me. And My revelations for a little gain. Whoso judgeth not by that which God hath revealed: such are disbelievers.
And We prescribed for them therein: The life for the life, and the eye for the eye, and the nose for the nose, and the ear for the ear, and the tooth for the tooth, and for wounds retaliation. But whoso forgoeth it (in the way of charity) it shall be expiation for him. Whoso judgeth not by that which God hath revealed: such are wrong-doers.
And We caused Jesus, son of Mary, to follow in their footsteps, confirming that which was (revealed) before him in the Torah, and We bestowed on him the Gospel wherein is guidance and a light, confirming that which was (revealed) before it in the Torah - a guidance and an admonition unto those who ward off (evil).
Let the People of the Gospel judge by that which God hath revealed therein. Whoso judgeth not by that which God hath revealed: such are evil-livers.
And unto thee have We revealed the Scripture with the truth, confirming whatever Scripture was before it, and a watcher over it. So judge between them by that which God hath revealed, and follow not their desires away from the truth which hath come unto thee. For each We have appointed a divine law and a traced-out way. Had God willed He could have made you one community. But that He may try you by that which He hath given you (He hath made you as ye are). So vie one with another in good works. Unto God ye will all return, and He will then inform you of that wherein ye differ.
Lo! Those who believe (in that which is revealed unto thee, Muhammad), and those who are Jews, and Christians, and Sabaeans - whoever believeth in God and the Last Day and doeth right - surely their reward is with their Lord, and there shall no fear come upon them neither shall they grieve.