I may have a unique perspective on this:

I come from a Coptic (Egyptian) Christian family, although born here in the states and not terribly religious, and I've had many encounters with those who most would label as westernized, moderate Muslims, and my overall opinion is that although there are many who are fully well-adjusted and contributing citizens, there are also many who may appear to fit in functionally, but their beliefs (religious) are still very much at odds with Western culture.

I went to an undergraduate university with one of the largest Muslim student clubs. They were notorious for being incredibly disruptive to the general student body. Although they were educated and came from well todo families, it was not uncommon for them to hold events at out university square where Imams would declare death to Israel, all the while club members wore shirts that said "Islam is the religion of peace." During Ramadan, they would block the main road around campus by organizing huge prayers smack dab in the middle of the road. They were known to disrupt talks by invited lecturers. Just by looking at their CVs you may think these young individuals are educated, social, well-adjusted, but observe their actions and their words and you'll see that it's not always the case.

Coptic Christians have been the victims of Muslim persecution of many years now - example - and I have been involved in bringing to light many of these atrocities by raising the awareness here in the states. I've gotten into numerous discussions and arguments with American Muslims here who refuse to acknowledge that Muslims were the ones who committed these crimes and/or that these massacres ever happened!

I've also spent much of my time in the UK where my experiences are similar. There are many, many Muslims in London, and again, many are fine and peaceful, but there are still non-insignificant numbers of them who refuse to genuinely assimilate by adopting the beliefs of western society. They run liquor stores or kebab shops and seem to operate just fine, but their core beliefs remain backwards. Only when they gather into groups or attend their mosques do they vocalize these beliefs. I have seen and heard it. Take a walk down Edgware Road in London and poll many of the Muslims there and you'll find that their core beliefs and ideals are concerning.

Again, I'll reiterate, many Muslims I know and am friends with are wonderful people. But it cannot be denied that there are many who refuse to fully assimilate, and who live in the western world only to reap the financial and resource benefits with no interest in relinquishing their concerning beliefs. We've all seen the Pew polls and I can say that my experiences and anecdotes support these numbers. Sure, the US has accepted tens of thousands of Muslims of whom the vast majority have not committed acts of terror, but that doesn't mean that many of the backward beliefs that many of them hold are suddenly gone -- they exist, you just haven't been looking in the right places.