Hi Dig,
I think the difficult question is to ask why it is that Christians and Jews mostly don't seem so keen on chopping people's heads off for being non-Christian or non-Jewish any more, while some (too many) Moslems still think it's kosher. Or halal, maybe.
For me, it comes down to a few things:
1. Islam finds evolution alongside changing, modern environments difficult. Around its edges, this generates heat.
2. Christianity's ability to resist change was broken during the reformation, the scientific revolution and the enlightenment. And so it mostly gets out of the way of the changes a society wishes to make for itself and no longer has the powers to resort to punishment/violence.
3. The Jewish tradition of living as a minority along a diaspora makes it necessary to fit in.
Thus, the Western revolution by which secular government delivers a permissive, individualistic model stands in contrast to the collective and restrictive identity of the umma (the brotherhood of Islam) interpreted through a Koranic lens.
In the end, Islam will submit. But these things can take centuries.