Islam is set up to specifically oppose Christianity on every important doctrine. For example, Christianity teaches that God is a Trinity—one God revealed in three persons (or manifestations). Islam, however, vehemently denies the Trinity as blasphemy (Suras 4:171, 5:17, 5:72-75). Accepting the Christian view of God is the only unpardonable sin in Islam, and condemns one to hell. While Islam has a high view of Jesus, it denies his divinity or that Jesus was the Son of God (Suras 9:30, 10:68, 19:35, 43:81-83).
There is a law of logic called the "Law of Non-Contradiction," which says that two contradictory things cannot both be true. At least one of them has to be false. This point of tension regarding the nature of God between the two religions is so great that it is clear that at least one of them must be false. Either the Trinity is a correct description of God as Christianity proclaims, or it is a false description of God as the Quran proclaims.
Muslims, as well as others, who have not studied the evidence for the deity of Christ find it understandably hard to accept Jesus as both 100% man and 100% God. Christians do not take belief in the deity of Christ on blind faith. The evidence itself has convinced many a skeptic. Simon Greenleaf, a professor of law at Harvard in the 1800's— a man who is considered the greatest authority on legal evidences in history —became a Christian after a thorough examination of the evidence. Anyone truly interested in religion should examine the evidence for yourself, the evidence demands a choice, a personal decision... for or against. If Jesus is truly who he claimed to be, then all humanity lives under the specter of judgment.
Muslims hold many mistaken views of Christian doctrine. Contrary to several passages in the Quran, Christians do not hold to three Gods! The Bible makes it very clear that there is only one God (Deuteronomy 6:4; Isaiah 43:10; Mark 12:29; 1 Corinthians 8:4, 6). Rather, there are three aspects to God's nature... the Father, the Son, and the Holy Spirit.
Also, Muslims think that the Christian term "Son of God" means that God the Father had carnal sexual relations with Mary, producing Jesus. That is incorrect. The term Son of God is a symbolic term only, implying the unique relationship Jesus has to God the Father.
There are other differences between the two religions as to the nature of God. To Muslims, God is distant and unknowable. His relationship to man is that of master and slave. He is not the personal God that Christians know and trust.
The God of the Bible is described as being love itself (1 John 4:7-21). The God of the Bible goes out of his way to find a single lost sheep (Matthew 18:10-14). And the God of the Bible opens his arms to offer comfort and assurance (Deuteronomy 1:31; Hosea 11:1-4; Isaiah 40:11; Matthew 11:25-30), as a father would for his children. This concept of God is absent in Islam. Islamic theology holds that God is good because he causes good. But goodness is not part of his essence.
Another very important difference is that the God of the Bible is holy — that is perfect in all respects and set apart from sinful humanity. He is perfectly moral, perfectly just, perfectly faithful, perfectly loving, all-knowing, etc. Another synonym for holy is pure (Hebrews 7:26).
But the God of the Quran does not always come across as holy. He changes his mind, changes his promises, and does not offer assurance of salvation. Allah is arbitrary (Suras 4:116, 5:18, 9:15, 25:51). Also, Allah deceives people (Bukhari 8:577 and 9:532).
Compare this to the God of the Bible, with whom it is impossible to lie (Hebrews 6:18) or to treat people unfairly. The God of the Bible is not arbitrary, but rather is perfect in his justice. If you do a search of the words holiness or holy as applied to God, you will see how dominant this concept is in all of Scripture.
Muslims today say that Allah is merely the Arabic word for God. While this is true, it is not the whole story. There is substantial evidence that Allah has roots in pre-Islamic paganism. There were 360 idols (gods) worshipped in Mecca at the time of Muhammad. The supreme god of the Quraish tribe (from which Muhammad came) was Allah. Muhammad's father's name was Abd-Allah, which means "slave of Allah." This supports the notion that the concept of Allah has its roots in pagan gods.
While not substantiated, some people say that Allah has elements of the pagan moon god, a dominant deity in pagan Arabia. To this day, the crescent moon is a symbol of Islam, and Muslims use a lunar calendar.
The Quraish tribe had a custom of praying five times a day to Mecca, had pilgrimages to Mecca, and had a sacred month. These things are an integral part of modern Islam. Such practices also tie Islam to pre-Islamic paganism. Actually, Islam appears to be an amalgamation of paganism, Judaism, Christianity, other world religions, accentuated by a healthy dose of power and politics.
In the modern world, Muslims recognize that Allah is not the God of the Bible. The evidence for that is the continual persecution of Christians in Muslim countries. Countries such as Malaysia have decreed that Christians may not even use "Allah" in their Bibles, books, or hymns. They often confiscate non-Muslim literature that uses the word "Allah." Why would Muslims take such a harsh view of Christianity if they thought they worshipped the same God as Christians? Those who say that Christians and Muslims worship the same God are incorrect.
In the two religions, God is defined differently and has different and contradictory attributes. The views of God between Islam and Christianity are incompatible.