Why do Christians drink wine and Muslims do not?
I have done a little research on this for you and I find that many Muslims disagree on what the Quran teaches about alcohol consumption. Most Muslims seem to prefer to err on the side of safety, however, so they do refrain from drinking alcohol because they believe the Quran forbids it.
The Bible, however, teaches that Christians are permitted all things, even though all things are not profitable for them. Christians are taught to refrain from anything that causes a brother to stumble. So, alchol is permitted, but drunkenness is not. Drunkenness is condemned many places in the Bible. Also, the negative results of drinking are put in the Bible as a lesson against drinking to excess. Alcohol is OK if it is consumed in moderation.
That said, there are several Christian denominations that also believe that alcohol should not be consumed at all. These groups believe that alcohol is dangerous and can be addictive and so therefore should be avoided. The Bible teaches that the human body is the temple of the Holy Spirit, so anything that harms the body is a sin against God. That would include smoking, drinking, drugs, eating to excess, etc.
The short answer is that The Bible does not forbid the drinking of alcohol, the Quran does.
Muslims belive that there was a prophet after Christ, named Mohammed. Mohammed was given a new holy book, the Quran, to serve as God's last message to humankind. The Quran, which muslims believe is the direct word of God, spoken to Mohammed through the Archangel Gabriel, forbids muslims to consume alcohol.