The real Islam is what you choose it to be.
Beliefs usually fall along a spectrum, with the underlying book providing the light source.
The difficulty is when you have people interpreting a book in a strict constructionist form. Societies and their moralities change. Bronze Age, Classical and Medieval ideas of right behaviour no longer fit our wants.
If you wish, save what you can from an elderly book. But no moral rules are immutable.
What we have here is a battle within Islam of the folks who have used that religion to control enquiry and human relationships with those who are adopting liberal ideas of individual freedom and secular law.