Question: "How can Christians be sensitive to Muslim/Islamic culture?"
Answer: As a preface to this article, please see our article on “What is Islam, and what do Muslims believe?” Knowing and understanding Muslims can go a long way to breaking down cultural barriers and dispelling myths about Islamic culture and beliefs. Note, while the below principles apply to most Muslims, in no sense do they apply to all Muslims.
Christians can develop genuine friendships with Muslims based upon mutual respect and interests. Some examples of extending friendship to Muslims include attending cultural or sports events with them; going together on picnics or on shopping trips; accompanying them to historic sites or museums; inviting them to one’s home; and accepting invitations to theirs. When Muslims come into the homes of Christians, certain things should not be done to avoid offense. Never offer food in which alcohol is a component and make sure any pet dogs are kept away from them (most Muslims consider dogs "unclean").
When in the home of a Muslim, especially if it is the home of a traditional Muslim, do not pass food with the left hand or point the soles of the feet toward them when seated in their presence. If possible, avoid using their toilet which could cause uncertainty in the mind of the host and/or hostess regarding "ritual uncleanness." In a Muslim’s home, dressing in a manner that Muslims consider immodest should be avoided. Building cross-gender friendships is another thing to avoid; it is fine to ask a Muslim husband or wife about the family, but (because of the possible implications) do not ask a Muslim man about his wife or a Muslim woman about her husband. Muslims do not usually want non-Muslims to compliment a baby or child—the parents may believe this will attract "the evil eye" and cause sickness. Neither the Qur’an nor the Bible should ever be laid on the floor or on the ground and nothing should be set on top of it. In addition, a marked-up or highlighted Bible is considered very disrespectful and irreverent to a Muslim.
The ultimate goal of befriending Muslims should be, for the Christian, to present the gospel of Jesus Christ to them. Those who are true disciples of Jesus were, at one time, "God’s enemies, but have been reconciled to Him by the death of His Son” (Romans 5:10). And we have been given "the gospel of peace" (Ephesians 6:15) to share with everyone in the world. That message needs to be undergirded by earnest prayer, accompanied by a blameless life and a bridge-building lifestyle, and verbalized by humble disciples of Jesus who sincerely love Muslims and are eager to share their lives and their Savior with them.