In the name of Almighty God/Allah, the Most Gracious, the Most Merciful. To give an example of how Islamists "refute" the ideals of democracy, or at least of true democracy, here is an Islamist cleric named Sheikh Salman al Oadah, a Saudi Wahhabi cleric who is widely read around the Muslim world. To the issue of democracy and its compatibility with Islam, he says this, http://www.faithinallah.org/democracy-in-the-context-of-islamic-law
To this I offer this rebuttal.
What this Islamist cleric misses, as do so many others, is that Allah says in the Quran "let there be no compulsion/coercion in matters of religion" (2:256). Governments only exist for the sole purpose of coercion. Governments create and enforce laws, and the only way to enforce laws is through coercion. That being the case, the very nature of Shariah, or Islamic Law, as per the above verse, is such that it CANNOT be implemented as the law of the land, over the masses, because that would involve religious coercion. Using the Qur'an as a governmental constitution is insulting to the divine nature of the Qur'an, and is indeed insulting to Allah Himself. The Prophet Muhammad, peace and blessings be upon him, ruled the city-state of Medina under the "Charter of Medina". In this charter there is not ONE verse of the Qur'an. Not ONE religious or spiritual 'law'. It established the city-state based on its citizenry, declared all citizens accountable to each other for support and defense, established a union between the various tribes of Medina, and established equality under the law regardless of religion. There was a large Jewish community in Medina at the time, and the charter specifically said, "To the Jews be their religion, and to the Muslims be theirs".
Shariah, or Islamic Law, is only law in the sense that it is the spiritual law that exists between the individual Muslim and Allah. It is what compels me to not eat pork, or not drink alcohol, or to pray 5 times a day, or to fast during Ramadan, etc. It is not and can never be imposed on others, regardless of whether they are Muslim or not. There are many different widely respected interpretations of Islamic Law including that of the Shia, Sunni, Sufi, Salafi, and many sub-groups within each of those. If Islamic Law is imposed as the 'law of the land' it is and will always be according to the interpretation of the predominant group. After all, if you speak to any hard liners within any of these groups they will tell you there's only ONE Islam and only ONE proper interpretation. So this majority will always inevitably oppress minority theological groups under any kind of "shariah law" based government. This has been the proven result in nations that profess to rule by "Islamic Law" such as the Wahhabi Kingdom of Saudi Arabia (where this particular cleric is from), the Islamic Republic of Pakistan, Afghanistan under the Taliban or the Islamic Courts in Somalia, just to name a few.
Muslims need to wake up and think before blindly following hack clerics. The brother is correct in his quoting of Allah, "The rule is only for Allah. He commands that we worship none but Him", and also, "Is it the rule of the times of ignorance that you desire? Who is better than Allah at ruling for a people who have certainty of faith". This is not an order to establish theological government, but it is to say that those who govern should themselves be personally and spiritually governed by Allah. It's no different than John Locke who speculated that an athiest should not be allowed to hold public office, because they are not accountable to anyone (ie God), and it was John Locke who was a primary influence of Thomas Jefferson, an American founding father and particularly the father of the American concept of separation of church (or mosque) and state.
Allah encourages Muslims to think for themselves and not to just blindly follow so-called scholars. Yes, scholars' opinions should be respected because they are people who have dedicated their life to studying our scriptures, however there is NO official magistrate or priesthood in Islam. Every individual Muslim is accountable to Almighty God directly and to no other. Allah says to not be like some of the Christians and Jews who took their priests and rabbis as lords besides God. The prophet explained that they did so not by praying to these people, but by blindly following what they say as the divine will of God. Muslims need to think for themselves, read, study and contemplate God's word in their own minds and hearts. God is nearer to us then our jugular vein, so why must we treat Him as if he is so distant and unattainable by the "lay" Muslims mind.
...And Allah Knows Best...