"Not by agreeing with it (that Islam and democracy are incompatible ,,,)".  It is imperative to call a spade a spade.  

Islam besides being a  religion, it provides an operation conduct for its adherents, like Sharia law.  May be there is absolutely nothing wrong with it.  That's why it is built into almost all Muslim countries for its societal operation. Islamic system will work if the majority of the population is of that affiliation. China has another form.
 
However, it is in diametrically opposite to be in concordance with western societies and hence the constant conflict. British born children of the  Pakistani immigrants, who were brought in by the then departing British in the 1960s to work in the mills and mines,  cannot comprehend the dichotomy  of their teachings and what is at large outside --with freedom to think or even dress. No opportunity to integrate in that society unless they have unwittingly come out of the closed society. 

Very complex circumstance.