Differences between Christianity and Islam
Question

What are the factors which cause a widening gap between Muslim and christian communities?.
Praise be to Allah.Basic Tenets of Islamic Belief  
There are many great factors that widen the gaps between Muslims and Christians. The differences in belief between us and them do not let us get close unless they give up their disbelief and misguidance, and join the monotheists who believe in One Lord and God, and bear witness that the Prophet Muhammad (peace and blessings of Allah be upon him) is His Messenger, and believe that `Isa (Jesus – peace be upon him) was a human being.
Basic Tenets of Christian Belief
These are the most significant deviations in their religion, which widen the gap between us Muslims and them: 

The Messiah (peace be upon him) is a god alongside God and that he is the second person of the holy trinity .
The Messiah is the son of God .
Divinity may be incarnated in humanity.
God is formed of three  coequal consubstantial divine persons, which is known as the doctrine of the trinity.
The Messiah (peace be upon him) was crucified by the Jews on the command of Pontius Pilate, and that he died on the cross.
The Messiah died on the cross as a ransom for mankind and as expiation for original sin .
The Christian attitude towards the Jews who disbelieved in Jesus (peace be upon him) and claimed that they crucified him and killed him, and they accused his mother Mary (Maryam - peace be upon her) of fornication – of which she was innocent – yet despite all that their attitude towards them today is one of support and loyalty, and their attitude towards the Muslims who venerate Jesus (peace be upon him) and his mother is one of enmity and disavowal.
Their distortion of the Book of God, the Gospel (Injil), whether they distorted the words by changing them or by adding words, or they distorted the meaning, and in doing that they attribute things to God that cannot be attributed to Him.
The doctrine of redemption, which is their belief that God sent His only son to redeem mankind from a sin committed by the father of mankind (Adam – peace be upon him), but God was unable to forgive his sin, so He sent His only son who had no sin, to sacrifice himself in order to do away with sin. This is an attribution of imperfection to the Lord of the Worlds and a denial of the fact that Adam (peace be upon him) repented and Allah saved the Messiah (peace be upon him) from death.
Their disbelief in the Prophethood of Muhammad (peace and blessings of Allah be upon him), even though he is mentioned in the Old and New Testaments.
Their belief in the soundness of the distorted Torah that they have in front of them today, which contains insults against God, describing Him as having shortcomings, and insults against the Prophets and Messengers, saying things that one can hardly dare utter, but we mention them in order to highlight the abhorrent nature of the disbelief that they follow. They describe God as weeping with regret for the Flood which drowned the people of Noah, until His eyes became sore, and the angels came to visit Him – exalted be He far above that.

They describe Lot (peace be upon him) as committing incest with his two daughters, and Noah (peace be upon him) as drinking wine until he became drunk and his `awrah (private parts) was exposed. There are even more foolish stories than that. 
See Hidayat al-Hayara fi Ajwibat al-Yahud wa’l-Nasara by Ibn al-Qayyim; Naqd al-Nasraniyyah by Dr. Muhammad ibn ‘Abd-Allah al-Sahim 
And Allah knows best.