Hi
I don't think Islam has a big problem with democracy now. But there is, in most Islamic societies, a problem with protection of minorities, modern human rights etc., though.
Islam was born as a state. And it's the major reason. Christianity was not born as associated with some form of a rule. It grew interconnected to monarchy from some point, but eventually it was forced to give it up.
While Christianity waited around 300 years to be even accepted in Roman Empire (and to become state religion in Armenia), and even more to actually become a state religion there,
Islam became a state religion during the lifetime of its founder, Muhammad.
Muhammad became de facto head of state, and at that a head of state with a mission to capture Mecca, wherefrom he fled.
I will not discuss the particular actions of Muhammad at lenght here. But, lets be honest: it was not a democracy.
After the death of Muhammad, the nascent Islamic State didn't call it quits, but elected successors of the Prophet (caliphs), who conquered half of the civilised world, including some of the richest provinces in the world, as Syria, Mesopotamia, Egypt. And for several centuries, the Muslim World was (with some splinter states) actually one, giant state stretching from Atlantic to China, and its armies operating from Volga river to Sudan.
The main judge, law-giver etc. was the caliph as the successor of the Prophet, but he named his deputies, judges (qadis). But obviously as time passed, the law got somewhat independent from the caliph. While it was undoubtly influenced by local traditions, it was all post factum islamised later on.
Because some jurists had an ingenious idea of basing all the law on Al-Qur'an and the sayings of Muhammad. The idea is quite logical. But it has two flaws. One is that it petrifies the socjety, and the second that actually, most of the sayings and deeds attributed to Muhammad were bogus. While Al-Qur'an was codified quite shortly after the death of Muhammad, that is not the case of hadiths, which were all sort of popular wisdom, private opinion, political propaganda stunts, and excerpts from local religious traditions that were attributed to Muhammad for giving them a bigger validity. We all know how influential a proverb is when accompanied with "... . Albert Einstein" signature. Not that Muslims weren't aware of that, some attempt at filtering the hadiths was done.
Hence, all the law was based on Al-Qur'an and sunna.
That started to change in the Muslim world, starting in 1798 with introduction of the Napoleonic Code in Egypt etc. And in late XIX century and early XX century there were serious attempts to modernise Islamic law.
But the trend at secularisation was stopped and reversed due to political circumstances (opposition to socialism, fight against Israel etc.) And the birth of modern islamist parties.
The great difference is that in the "Christendom", even if some party is "Christian", it means fairly little. There aren't really any Christian world-wide rules concerning the state and society apart from some basic rules. The Church has its teachings, but canon laws are not really comparable, and its demands are either very general or connected to some very specific cases; also, the demands are changing.
In Islam there's shari'a, and while there are different schools (madhhabs), the differences are not really great among them. And I know some jurists are much more progressive, but in general, it's a factor that's bringing islam and Islamic world back.
And it's not the problem that actually shari'a envisions world ruled by caliph, because there's no caliph, so for the time being sort of democracy is ok. And in fact there was shura - the first caliphs were elected by a sort of a gathering of Muslim elders, and there were other instances of democratic principle. But as long as shari'a has some authority, and it has and it's not really threatened much, it will be eclipsing human rights. And I do think it's a bit telling that in Egypt, the Muslim Brotherhood was campaigning in 2013 against the project of the constitution also by opposing the concept of human rights. Not that the current goverment is so dedicated to them.
We are used to associate democracy with freedom of speech, confession, gatherings, protection of the minorities etc. But it's not necessarily so.
http://www.pewforum.org/2013/04/30/...ligion-politics-society-beliefs-about-sharia/
so see:
only in Kosovo (slightly) more people view shari'a as man-made construct based on the Word of God than as Word of God.
only in Iraq, Morocco and Tunisia (close to in Turkey and Indonesia) more people believe there's more than one interpretation of shari'a.
in most of Muslim in the countries polled
(apart from the post-socialist ones in Central Asia and Europe, Turkey, Lebanon, Tanzania, Chad, Guinea Bissau and Tanzania, but it's very close to half in Chad and Guinea Bissau)
people want to make shari'a the law in their land. That includes also countries in which Muslims are a minority. Including a very small one.
In all countries apart from Kosovo and Bosnia people want qadis to decide on family issues.
In Tajikistan, Malaysia, Thailand, Pakistan, Afghanistan, Palestine, Egypt, Jordan, Bangladesh
(and close to in Lebanon and Indonesia, but even Tunisia)
people favor stoning as a punishment for adultery.
In Malaysia, Afganistan, Pakistan, Egypt, Jordan, Palestine
(but close also in Bangladesh, Lebanon and Iraq)
people are majorly in favour of killing apostates.
Only in Lebanon and post-socialist countries (Bosnia, Kosovo, Albania, Azerbaijan, Kazakhstan) more Muslims are more happy than sad with shari'a not being closely implemented.
Actually, if a majority of people in democratic elections, would decide they want to kill gays or apostates, that would technically still be a democracy if it was possible to decide to change this law. But if people want shari'a to be implemented, it is af they were saying "no, we don't want to decide".
Now, if a majority of people do not want democracy, is it still a democracy?
I guess it is if democratic ways of changing this decision still exist. But it may be hard to come back.