I think its possible for intelligent, decent people to square the contradictions between a traditional worldview and the demands of a liberal society. The problem is that many people aren't all that intelligent. It's clear that the thousands of Europeans who have gone to fight for ISIS haven't been able to function in the face of these contradictions. I don't accept that Islam is inherently more contradictory to Western society than other worldviews. But it does seem to be more persistent as an organizing principle than some.
I think the USA has slightly better success in integrating traditional Muslims, but a big part of our success has been in attracting a relatively intelligent and functional set of immigrants. On the one hand its inhumane not to accept refugees from warzones in Syria, Iraq and Afghanistan. On the other hand, I worry that we wont be so successful at integrating a broader, less educated population. We accepted less than 200 refugees from Chechnya and THREE of them turned out to be terrorists and mass murderers. Obviously, more than 98% of Chechen refugees are not mass murderers, but I still don't like those odds.