A couple months ago Robert Karp asked this question. I initially meant this as a comment to that post, but it developed into something bigger, so a blog post makes more sense.
For the most part, Christianity has gotten past its bronze age stage. There are still pockets of severe repression, but not so much anymore. People make a lot of prayer in the classroom, commandments on church lawns, and "In God We Trust," but these things are nothing compared to what was going on a few hundred years ago.
Islam, on the other hand, largely has not moved forward. As you say, it is mostly contained to "third world" countries, which is true, but of late a lot of those folks have taken it upon themselves to emigrate to and challenge the customs of the 1st world countries. The exception to the last sentence is the American born children of these people (or ones mostly raised here). They seem to have settled the clash between their religion and Western culture.
What would be dangerous to our society is if those backward ideas take hold. People say it can't happen here, but already in some European countries there are whole areas where it's simply not safe to travel if you're indoctrinated in the Western way. The most immediate problem is that of insular communities; those which might have an ultra fundamentalist Muslim majority, where police and other secular authorities are subservient to powerful clerics.
This actually already happens in communities with ultra fundamentalist Christian or Jewish orthodox majorities. It just doesn't get talked about much because they tend to keep to themselves. As far as I'm aware, there are no ultra fundamentalist Muslim majority communities as of yet (or Muslim majority of any level of piety for that matter), so whether or not they'd do the same thing remains to be seen.