There are divisions in Islam.
There isn’t a unique lecture of the Koran. Because there is no Pope in Islam, no Rome (even if Saudi Arabia wishes to be seen as), a lot of scholars debate the faith and its practise. The best known is between Shiite and Sunnite, but Islam goes from pacific Sufis to the more reactionaries Wahabists and Taliban for the most extremists.

The main problem to reform Islam is the book was written by the Prophet himself. Christianity rules were fixed 300 years after Christ, and base on documents written 60 years after his death the resurrection. Knowing that Christ died at around 33 years old and his disciples were probably around the same age, that let the atheists like me questioning the validity of such witness, but that is another debate…

The New Testimony is the base of Christianity, not the Bible, which is recognised by the Christians (and the Muslim) is questionable. The words of Christ himself are depending of the witness. The Muslims haven’t such possibility of doubts.
But interpretations of the words are still possible, and all the Muslims intellectuals during the centuries never failed to do it.
Islam and Democracy are mixable. Who could have believed that the Catholic Inquisition would melt, that people like Torquemada would give path to Las Casas.
Ok, it cost the extermination of all South and Central America, but all religions could evoluate.