Islam is even less of a monolith, as PP have pointed out, than Christianity is. There are some beliefs that are held in common - such as the idea of the Qu'ran as a revealed text, for example - and others where there is little to no agreement, whether that's the authenticity of various hadiths (for want of a better description, "stories" - not meant in a derogatory way- about the Prophet and what he did or said, passed down through a chain of individuals, which can then be extrapolated from in order to explain ideas or processes etc not covered in the Qu'ran) or the sort of shari'a law they follow, or which succession after the Prophet was favoured.
Most people are aware of the Sunni/Shi'a split, but fewer are familiar with, for example, the Ahmediyya (persecuted significantly, especially in Pakistan) or the Alawites, both of whom consider themselves to be Muslim, but both of whom are considered somewhat heretical but other Islamic sects. As is often the case with religion, believer on believer violence is far more extreme in many cases than violence between religions.
HOWEVER, what all sects have in common is the attitude towards the Qu'ran as a revealed text: those of you familiar with church speak will know the difference between Christian fundamentalists - that everything in the Bible is literally true - and Christian modernists (that some of the Bible can be explained by treating it as allegory, rather than as literal truth). Obviously, that's a bit of an over-simplification for the purposes of this post, but there isn't a mainstream Islamic preacher, much less a sect, that accepts the Qu'ran for anything other than a revealed text. Because it's revealed, this means nothing may be changed or altered (as it has come directly from God through the Angel Jibreel to Mohammed) and as early as maybe the ninth century CE (so 200 years after Mohammed) scholars decided that "the gates of ijtihad" needed to be closed: basically, that there could be no more interpretations of God's laws, because all the main questions had already been answered. Essentially, this has made it very difficult, then (though this assertion is questioned by some Islamic scholars) to disrupt the orthodoxy on various aspects of religious law etc
Initially, though, the Qu'ran is actually a really ground-breaking text in terms of women's rights - essentially, it wasn't just a religious text, but also more or less a political blueprint for how to create a Godly state, so it contains lots of information about inheritance etc People make much now - and rightly so - about Islamic inheritance laws, and that women are entitled to a smaller portion than men. However, at the time it was revealed, this was a major concession - consider the position of women in 7th century Europe with regard to inheritance entitlement!
The issue of polygamy is also much misunderstood - firstly, it was only permissible any way if a husband could undertake to treat his wives exactly the same. Some scholars have argued that this instruction actually means that it is never permissible, because it is not possible for someone to give the same amount of love in the same way to two women. However, the more traditional interpretation looks at it that this must be in a material sense - that the wives must get the same standard of living etc, and the same time spent with them. The real issue here, though, was the inclusion of polygamy at all - it's not laid down in the Qu'ran as a means of men's advantage, but rather, to ensure that widows and orphans (who traditionally got a very raw deal, especially in this period in desert societies) would gain proper status and protection.
The problem is, though, that although these things revolutionised Arabian peninsular society in the 7th century, and spread rapidly through to Europe as a result of the spread of Islam (which was, of course, one of the reasons it was so important to have provision for widows and orphans - there was a lot of fighting, both internally and externally after the death of Mohammed until about the mid 8th century) revolutionising society there, it's arguable that these safeguards are no longer necessary in the 21st century anywhere in the world. Statements intended to be revolutionary in the time that they were first revealed have instead become reactionary, and tools for the oppression of women today.
I would argue that this is because continual interpretation and reinterpretation hasn't been allowed to take place wholesale- but then, I would say that, wouldn't I?!
In some places - Afghanistan, for example, there are cultural practices in some areas that pre-date Islam's appearance in the region: but are today attributed to Islam. A similar phenomenon is FGM - people in general (as opposed to just those who traditionally practice it) widely consider this to be an "Islamic" practice, whereas in fact, it's a cultural tradition, and has nothing to do with Islam whatsoever. Covering the face is also a cultural tradition, and has no basis in Islam whatsoever - it was the practice of wealthy Byzantine women in the 4th and 5th centuries, and was adopted for status by some of the conquerors. In fact, the Grand Imam of al Azhar, the oldest Islamic university, who is pretty much a hard nut when it comes to shar'ia interpretations, actually verbally attacked a group of Cairo school girls when he gave a lecture to them - he told them that covering their faces was unIslamic: and full face covering, including the niqab, is banned at the university. However, there are far more cultural behaviours, particularly surrounding attitudes towards women, that have their bases within the original text of the Qu'ran (which, by the way, for believers, should always be read in Arabic, even if the individual doesn't understand that language - think of the wars that started in Christendome over whether there should be translations of the Bible in the vernacular!) and can be traced clearly from some of the suras.
The problem, as ever with religion, is not necessarily the religion itself, but the ways in which is it used: and, inevitably, the ways in which it is misused by the patriarchy. However, in Islamic countries (and I mean countries that self-define as Islamic, not have significant populations of Muslims or Muslim majorities) the religion, and more importantly, the uses of religion by the elites, has had a significant influence on the post-Islamic culture, and this is the effects we have seen across Europe. I don't think it's possible to quantify precisely the break down of religion vs culture, but it is easy to spot sometimes the religious origins of some of the cultural behaviour. This is why I think it's disingenuous at best, and incorrect at worst, to try to separate the two in these instances we have been discussing across these threads.