Christianity at least tries to change, to a degree. though it clearly has a hard time doing it.
I think with Islam it literally goes against the religion to change any word of it, doesn't it?
That's really a sectarian thing. Saying that "Christianity tries to change, but Islam does not" is a pretty massive oversimplification, given the enormous amounts of very, very traditional Christian sects. Some groups have succeeded at changing in light of modern social or philosophical developments, but until the modern era, any attempt to change Christian doctrine or worship was met with violence.
Most Muslims do not live their lives in exact accordance to the Qur'an, obviously. I can't tell you if this is because of belief or because of practicality, but given that nearly all non-fundamentalist Muslims live in Muslim countries, I'd reckon it's because most Muslims aren't anywhere near as religious as the Taliban or ISIS. Another major issue is the treatment of the Hadiths. As you probably know, those are a collection of sayings allegedly made by Muhammad in his lifetime. Unlike the Qur'an, the Hadiths weren't written in or immediately after Muhammad's time, and include a lot of mysticism and contradiction that suggest multiple authorship. Most of the more odious prescriptions in Islam (including essentially everything about rape) come from the Hadiths, and various Muslim groups disagree hugely about which Hadiths (if any) should be accepted.