Really? Your religious life IS your civil life in Islam. They are one and the same thing. Now a lot of Muslims in the US (and here in the UK) came here precisely to get away from that mindset. Fair enough - they are good people, valued in the community, work bloody hard and have a sense of pride in that, their families and their adopted country. It is zero surprise to me that they voted Republican. They have the same values, as people.
Others - especially refugees - want to keep that mind set. They came here to escape something intolerable and brought it with them. Two very different outlooks. We see it here a lot, you've heard the stories of "Muslim gangs" attacking people in the streets. What is very rarely mentioned is how severe these attacks are - not on whites, but on apostate Muslims.
Most Christians do NOT follow many of the rules of their faiths. Premarital sex, adultery, abortion, drunkenness, hate, blasphemy are just a few misdeeds.
For a muslim there is a big benefit of exchanging his living situation, for an opportunity in the UK or the US. Moving from 3rd world to 1st world instantly.
A lot of them do just that. It is often 2nd generations that turn out to be fanatics, and problem people. They did NOT consciously make the tradeoff. Their parents did. They are lost culturally in the free new land, they had nothing to do with selecting.
Islam at it best is barely okay and at its worst it is hideous. But it is what they have, and what they must make accommodations away from.
I don't assume muslims are any more complete in following their rule book, than are Christians. I give them the benefit of doubt until given reasons otherwise. Then the hammer falls.
A lot of show of being devout muslims, is show for neighbors and family. You fly into Iran or Saudi from the west, and the females don required scarves, for instance. They wear them in country, not because they devoutly BELIEVE, but to avoid trouble.
Don't assume all muslims strongly believe their religion's rules.
Remember many came to America initially to find freedom FROM imposition of state religion on one's family, neighbors and friends. It is in our DNA.
In historical terms it is pretty recent and many places don't fully get it. Last century the Lutheran church was the Swedish state's official recorder of births, marriages, deaths etc. As well as proficiency in Biblical knowledge.
Catholicism, Lutheranism and Anglicanism are official state religions in many places to this day.