Islam is an Abrahamic faith.
What was the faith of Abraham? It was and is the faith of Jesus Christ.
Some have apostatized from that faith in various ways over time. The heirs of apostate creeds are not as accountable before God as are the originators of such creeds; "the sin be upon the heads of the parents" when they teach their children not to believe the fullness of the Gospel.
Remember the Abrahamic covenant, in which the Lord promises, in part:
And in thy seed shall all the nations of the earth be blessed; (Genesis 22:18)
How can God fulfill His promise that all nations would be blessed in Abraham's seed, if the Muslim could not in some measurable way be blessed through the posterity of Abraham? Therefore God delights to bless His children through His covenants, be they of whatever nation or religion or circumstances they may.
Part of that covenant was that the Lord would gather those who have been scattered from Israel. That gathering is taking place today and is more of a spiritual gathering than a physical one. If there is a spiritual work of gathering those who have strayed, does this not apply to those who once had more of the faith of Abraham, but have since departed from parts of it? It does. God will force no one to accept more than he is willing to accept, and refusing the Lord leads to diminution, but He does extend His mercy and His offer of repentance and forgiveness to all people, as the Apostle Peter expressed regarding the conversion of Cornelius.
Note that the Scriptures also prophesy that all who have erred in doctrine but remain at the Lord's Second Coming will arrive at the full knowledge of Christ:
And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. (Hebrews 8:11)
Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ: (Ephesians 4:13)
As I mentioned in another answer, God rewards people according to the degree of their faith and diligence in Him. This means that salvation and exaltation (the highest salvation) is not a binary. The Lord said, "In my Father's house are many mansions (John 14:2)." Therefore there are degrees of blessings He gives for degrees of faithfulness.
If a Muslim keeps the Lord's law of the fast, he will be blessed for doing so. If a Muslim keeps God's law of chastity, he will be blessed for doing so. If he gives to the poor in keeping with the Abrahamic tithe, he will be blessed according to the Lord's promise. How did the Muslim know about fasting, or chastity, or almsgiving? Through the commandments the Lord delivered to father Abraham.
Thus we see a beginning of the blessings of Abraham flowing through his posterity who keep the commandments of God to bless all nations of the Earth.
God reserves the highest blessings for those who show Him the highest fidelity and valor, but He does not refuse to bless those of a lesser understanding and commitment according to the heed and diligence which they give to abide by all that they become aware of that comes from Him.
Note that sanctification implies becoming holy, which would require the constant companionship of the Holy Ghost. This can only be authorized by ordinance; although a man may be justified by faith according to the laws that have thus far been revealed to him, sanctification requires ordinances by the power and priesthood of God.
For precept must be upon precept, precept upon precept; line upon line, line upon line; here a little, and there a little: (Isaiah 28:10)
Therefore we should not suppose that a Muslim is not blessed for obedience to the laws and commandments of God as far as he knows them. Salvation and blessing are not an all-or-nothing proposition, reserved only for those who--Calvinistically, we must suppose--happened to inherit the fullness of the "true faith", while all others are elected by the wrath of God to be damned, no matter what they do. The claim that God does not bless His children and entice and assist spiritual growth in people is completely unfounded and presupposes that the entirety of Christianity is congruent with Calvinism, which it is not. What we do in this life really matters, and we have freedom of choice, including freedom to convert and upgrade our spirituality as we each learn more and become aware of things we hadn't considered before.
So shall he sprinkle many nations; the kings shall shut their mouths at him: for that which had not been told them shall they see; and that which they had not heard shall they consider.
(Isaiah 52:15)
Paul affirms that this is speaking about the role of missionary work towards those who had not so much as heard of Christ previously:
Yea, so have I strived to preach the gospel, not where Christ was named, lest I should build upon another man’s foundation:
But as it is written, To whom he was not spoken of, they shall see: and they that have not heard shall understand. (Romans 15:20-21)
Therefore evangelism is to play a major role in conversion to Christianity, which may be by degrees as the Lord displaces darkness and the scales shall fall from the eyes even of those who have persecuted us, and yet have found repentance. The reformation was this kind of iterative process of realization and some repentance, which prepared the way for the Restoration spoken of in the Scriptures. Therefore predestination is false and there is no good cause to be contentious, prideful or spiteful towards those of another faith background. Christians most of all should teach and exemplify an attitude of understanding towards all men. The Lord came into the world not to condemn the world, but that the world through Him might be saved, and He commands us to love even as He loved.
The self-righteousness of many self-denominated Christians who suppose predestination to be the case is itself a pagan creed that remains to be shattered. Distinguishing between the way that is Christ's and what is not of Him may even in some cases take professing Christians the better part of a millennium to learn.
All who keep any of God's commandments will begin to grow and be blessed by their faithful choices. Those who keep all of God's commandments will be justified by the Lord's grace through their faith, and those who do all His will will receive eternal life.