1. Equality of all human beings in the eyes of the law. In particular, men and women are equal in the eyes of the law, and members of all religious groups are equal in the eyes of the law.
2. Freedom of beliefs in general, and religion in particular. A person is free to choose the faith and the manner of his worship.
3. Freedom of expression and freedom to dissent. Freedom to intellectually scrutinize any doctrine, including a religious one.
4. Belief in democracy as the ideal mode of governance.
Once again, while no society has arrived at this perfect ideal in practise, most modern nations would agree to all four points in principle.
But not Islam. Not Shari'a. Islamic law (Shari'a) is categorially and emphatically opposed to ALL 4 axioms of modern civilization. Let us inspect each one in turn.
1. Shari'a law denies equality to women and to non-muslims. In particular, the testimony of a woman is worth only half of a man, and the testimony of a non-muslim is worth only half of a muslim. This is agreed upon by all 4 schools of Sunni jurisprudence (Hanafi, Shafi, Hanbali, Maliki).
2. Shari'a law does not allow a muslim to leave his faith. The penalty for a muslim who leaves Islam is death, according to all 4 schools of Sunni jurisprudence. This is based on numerous Hadith where either Muhammad directly says that those who leave Islam must be killed, or his close companions bear witness to him having said so. In several Hadith, this sentence is actually carried out (i.e., a former muslim is put to death, and this is recorded in the Hadith).
Shari'a law also does not give non-muslims the right to build their places of worship. It does not allow idol worship as a means of worship. Strict implementations of shari'a law demolish idols, such as the Taliban's destruction of the centuries old Bamiyan Buddhas.
3. Shari'a does not allow any sort of open discussion of Islam. Criticism of Islam and the Prophet Muhammad is punishable by death. This is part of law even in countries that do not have full fledged Shari'a law, such as Pakistan. Under Pakistan's Tauheen-e-rasool (literally "disrespect of Prophet") act, any criticism of Muhammad is punishable with death.
4. Shari'a is a strict alternative to democracy. In other words, Shari'a posits itself as a political system, and does not recognize the legitimacy of any other political system such as democracy. Every single school of Islamic jurisprudence says governance by Shari'a is the only acceptable form of Islamic government. Democracy is categorically rejected as an acceptable system of governance. Almost every Islamist writing pours scorn on democracy and secularism as "western inventions" that are "contaminating the muslim ummah."
So Islamic Shari'a law is opposed to all four basic axioms of modern civilization as we know it. It is not a coincidence that Islamic societies "look very different" from free societies. I have not even gone into subtleties such as barbarity of punishments (such as stoning to death, chopping limbs etc. which are imposed under Shari'a law). I am speaking simply of the basic axioms that underlie modern human civilization and society and which mankind has generally come to agree upon, with the one exception of Islam. Islam rejects all these axioms.
...With thanks to Dharmaveer