Christianity also has the very convenient line "Render unto Caesar the things that are Caesar's, and unto God the things that are God's"[1] in the New Testament that basically codifies separation of church and state into the religion. Islam has nothing equivalent, in fact more so the opposite.

1.https://en.wikipedia.org/wiki/Render_unto_Caesar

The fact that a rule is in the OT doesn't mean it is Christian belief that it is applicable. In fact, the rejection of most of the OT Jewish law as inapplicable to non-Jewish Christian is itself in the Bible (Acts 15).

The difference is that the New Testament explicitly rejects at least part of the Old Testament's rules: http://crossexamined.org/cherry-picking-the-bible-are-christ....

Moreover, the elevation of faith over adherence to law as the path to salvation also has the effect of deemphasizing the latter.

And yet, there is a nice quote, attributed to Jesus himself, in the New Testament, saying that "I am not here to replace the old laws". Which can be interpreted as meaning that the OT still is relevant.

The difference being the New Testament was written decades after Christ's death by apostles who expected worldly salvation a lot earlier, and so the stories are ripe for exaggeration and misremembered details (and the parts that the Catholic Church destroyed because they were incompatible with their ruling ideology but we'll let that go for now).

As for the Old Testament: how many Christians keep kosher?

Islam's founding story is much more straightforward: Angel tells Muhammed to transcribe a book that exists word-for-word in heaven. No ambiguity there.

Exactly no ambiguity. The Quran and the Hadiths clearly state things as they should be and leave little to ambiguity, and that is why reform is extremely difficult within Islam. When the book clearly says that it is the one and true word of God and is perfect, how will you justify reformation. Saying that religion is not a political issue in the middle east is a complete misunderstanding by people.

I never said religion is not a political issue in the Middle East, I meant that you cannot simply fix the Middle East by "fixing" religion. You also cannot fix America's dysfunctional government by making it more like Singapore's. Whatever happens must be compatible with the cultures of the people living there, not what outsiders would prefer it to be. Come to think of it, that's a hefty reason the region is such a mess in the first place.

Edit: the Hadiths are continually debated for accuracy and adherence as they have varying levels of perceived legitimacy, somewhat like interpretations of passages in the Christian New Testament.

Trying to justify one terribly gone wrong political ideology with another isn't a good way to justify an argument. And in the modern age, many Christian majority nations have successfully created secular states, something Islamic states won't and never will consider unless major reform can occur.