Why won't Muslim governments who won't let their people do anything "un-Islamic" just back off, let the people do what they want, and if "Allah" wants anyone punished for it, let him do it for himself? It's like they're saying "Allah obviously can't take care of things himself, so we're going do it for him." Seems like that would be an insult to him.
I heavily edited your question before posting it to this site because the way it was originally worded would be highly offensive to a Muslim without any benefit.
The question could be turned around and said, "Why doesn't the United States government allow its people to do anything un-constitutional?" The question is indirectly stating that anarchy, living without a system of law is preferable to living under law. Such has never been the case.
Laws define what is right and wrong. "What shall we say then? Is the law sin? Certainly not! On the contrary, I would not have known sin except through the law. For I would not have known covetousness unless the law had said, "You shall not covet."" (Romans 7:7). Law doesn't make things right or wrong, it simply states what is accepted as right or wrong. For example, murder is clearly wrong. The law explains that murder is punishable, but it didn't make murder wrong.
Sin is defined as the breaking of law. "Whoever commits sin also commits lawlessness, and sin is lawlessness" (I John 3:4). Hence, where sin exists law exists because sin is the breaking of law. "Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned -- For until the law sin was in the world, but sin is not imputed when there is no law. Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come" (Romans 5:12-14). Paul's point is that even before the Law was given to the Israelites at Mount Sinai, there was still law in the world. How can he make the claim? Because men were sinning. Law has always existed.
Now why don't Muslim's tolerate the breaking of Islamic law? Because this is the law that they have placed themselves under. You and I might disagree with the points of their law. We can argue that certain features do not correctly define what God has said is right or wrong. But we cannot justly advocate that their government or any government ought to allow people to do anything they desire. "Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves. For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same. For he is God's minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God's minister, an avenger to execute wrath on him who practices evil. Therefore you must be subject, not only because of wrath but also for conscience' sake" (Romans 13:1-5).
It is true that Christians will not be able to completely submit to Islamic law. From a Christian's viewpoint, Islam is a man-made religion. When there is a conflict between the teachings of Islam and the Bible, the words of God will always take first priority. When the Jewish government issued an order, "And they called them and commanded them not to speak at all nor teach in the name of Jesus. But Peter and John answered and said to them, "Whether it is right in the sight of God to listen to you more than to God, you judge" (Acts 4:18-19).
One point that places Christians in conflict with Islamic law is their forbiddance of leaving the Muslim religion. Christians are commanded to teach about Christ and convert people to the way of Christ. Islam only has conditional tolerance of other religions. In Surah 2:256 it says, "Let there be no compulsion in religion. Truth stands out clear from Error; whoever rejects Evil and believes in Allah hath grasped the most trustworthy hand-hold, that never breaks. An Allah heareth and knoweth all things." But a non-Muslim in a Muslim country is required to pay extra taxes, call Jizya, because of their rejection of Islam. In Surah 9:29, "Fight those who believe not in Allah nor the Last Day, nor hold that forbidden which hath been forbidden by Allah and His Apostle, nor acknowledge the Religion of Truth, even if they are of the People of the Book, until they pay the Jizya with willing submission and feel themselves subdued." "People of the Book" is Islam's way of referring to Jews and Christians. It should be clear that Islam is tolerant of other religions only so long as those of other religions acknowledge that Islam is better. Obviously this will place Christians in direct conflict with the state goals of Islam.