In Dearborn Michigan, we can see populations of American Catholics with largely Polish backgrounds mingle with Lebanese-American Christians and Muslims in the same neighborhoods.
The young people tend to share very common social values. While the high school does necessary things to accommodate Ramadan, for example, when it falls during football season (because fasting teenage athletes are not good for winning championships), and while many restaurants default to halal food preparation, the city feels very American.
And as you say, nothing about the theology of those Catholics or Muslims has changed. They have adopted the identity of residents of Dearborn, while retaining their religious identities and accommodating them.