Religions do not tend to be unchanging monolithic entities. They adapt and change. At any given point in time their may be multiple versions or strains of a particular religion. A single religion can have various interpretations, many of which may be incompatible with each other. From what I've seen, people conveniently tend to make religion whatever they want it to be.
Why do you think Islam is different?
The answer to your question is too complex for a single post. The short answer is that Islam isn't so much a religion as it is a totalitarian political ideology with a religious component.
I'll try to give you a more detailed explanation for why I think Islam is different.
It's compulsory for Muslims to follow the sharia - a highly specific legal and political plan that governs every aspect of the Muslim's life (and I mean EVERY aspect). Even rules for things as simple as washing yourself or the elimination of bodily waste can be found in the sharia. For Muslim's living in a non-Muslim liberal democracy, the sharia takes precedence over the law of the land when the two conflict.
Islam's stated goal is world domination, not peaceful coexistence as equals with the disbelievers. The Quran commands Muslims to spread the faith by force:
"8:39. And fight them until there is no more Fitnah (disbelief and polytheism: i.e. worshipping others besides Allah) and the religion (worship) will all be for Allah Alone [in the whole of the world]. But if they cease (worshipping others besides Allah), then certainly, Allah is All-Seer of what they do.8:67. It is not for a Prophet that he should have prisoners of war (and free them with ransom) until he had made a great slaughter (among his enemies) in the land. You desire the good of this world (i.e. the money of ransom for freeing the captives), but Allah desires (for you) the Hereafter. And Allah is All-Mighty, All-Wise.
9:29. Fight against those who believe not in Allah, nor in the Last Day, nor forbid that which has been forbidden by Allah and His Messenger and those who acknowledge not the religion of truth (i.e. Islam) among the people of the Scripture (Jews and Christians), until they pay the Jizya with willing submission, and feel themselves subdued.
9:33. It is He {Allah} Who has sent His Messenger (Muhammad) with guidance and the religion of truth (Islam), to make it superior over all religions even though the Mushrikun (polytheists, pagans, idolaters, disbelievers in the Oneness of Allah) hate (it)."
The above are only a few examples of commands to spread Islam that are in the Quran. Unlike the descriptive passages of violence in the Bible, the violent passages in the Quran are prescriptive and open-ended. That is, they still apply today. This is an important distinction and it explains why you cannot find a single example of a Christian or Jew invoking scripture to justify violence, but examples of Muslims doing so are commonplace.
The Quran itself is not subject to interpretation because Muslim's are commanded to adhere to a strictly literal interpretation. The scriptures in the New and Old Testaments are considered by Christian's and Jew's to have been "inspired" by God, and thus subject to interpretation, whereas the Quran is considered by Muslims to be the direct word of God, and as such, not subject to interpretation. For that reason, the Islam practiced today is essentially unchanged from the Islam practiced in 610 AD. That's why you see floggings, stonings and amputations still being practiced in Muslim countries that are under the sharia today.
In addition to the fact that Islam is a supremacist ideology, the Quran forbids Muslims from befriending disbelievers. This is one of the reasons that many Muslim immigrants fail to assimilate when other immigrants like Hindus and Buddhists are assimilating easily. From the Quran:
5.51. "O you who believe! do not take the Jews and the Christians for friends; they are friends of each other; and whoever amongst you takes them for a friend, then surely he is one of them; surely Allah does not guide the unjust people."
3.38. "Let not the believers Take for friends or helpers Unbelievers rather than believers: if any do that, in nothing will there be help from Allah: except by way of precaution, that ye may Guard yourselves from them..." This last part means that the Muslim is allowed to feign friendship if it is of benefit. Renowned scholar Ibn Kathir states that "believers are allowed to show friendship outwardly, but never inwardly."
3.118. "O you who believe! do not take for intimate friends from among others than your own people, they do not fall short of inflicting loss upon you; they love what distresses you; vehement hatred has already appeared from out of their mouths, and what their breasts conceal is greater still; indeed, We have made the communications clear to you, if you will understand." This verse not only warns Muslims not to take non-Muslims as friends, but it establishes the deep-seated paranoia that the rest of the world is out to get them.
9.23. O ye who believe! Choose not your fathers nor your brethren for friends if they take pleasure in disbelief rather than faith. Whoso of you taketh them for friends, such are wrong-doers" Even family members are not to be taken as friends if they do not accept Islam. (This is the mildest interpretation of this verse from the 9th Sura, which also advocates "slaying the unbeliever wherever ye find them").
53.29. "Therefore shun those who turn away from Our Message and desire nothing but the life of this world."
I'm not saying that all Muslims adhere to those commandments. One of the similarities Islam shares with other religions is that not everyone is all that serious about practicing the religion. Some are Muslim in name only, others only take part during religious holidays, some don't care, some want no part of jihad, etc. And in many non-Arabic regions in the world, Muslims have no idea what the Quran says because they are unable to read it. Most Qurans are written in Arabic.
Regarding your point that "
at any given point in time their may be multiple versions or strains of a particular religion. A single religion can have various interpretations, many of which may be incompatible with each other." This is true of Islam as well. But like the different Christian denominations, the different sects of Islam share a common core.
These are just a few of the reason why I don't believe Islam is capable of coexisting within Western liberal democracies. There is so much more. To gain a better understanding of Islam, I recommend The Complete Infidel’s Guide to the Koran by Robert Spencer,
and Cruel and Usual Punishment: The Terrifying Global Implications of Sharia Law by Nonie Darwish.
Just because Western liberal democracies and religious pluralism have not prevailed in predominantly Islamic cultures does not necessarily mean Islam is fundamentally incompatible with it. A similar argument could have been made about other religions before they encountered Western democracy. But the religions adapted.
Why are you convinced Islam is different?
Middle East Quarterly Spring 2007, pp. 71-79; Can There Be an Islamic Democracy? Review Essay
by David Bukay
http://www.meforum.org/1680/can-there-be-an-islamic-democracy
Political Science Quarterly, Summer 1984, p. 214; Will More Countries Become Democratic?
Samuel P. Huntington
http://www.cooperativeindividualism.org/huntington-samuel_will-more-countries-become-democratic-1985.html