Not sure what you mean by “succeed” -
they WILL dominate and take over when America loses its moral grounding to secularist relativism.
Secularist relativism won’t stand up to the “wrong” that is Islam, and they will “win” by default, by not facing any opposition.
This is a recurring historical event, decadent, flailing cultures get taken over by those that have firm, set standards and beliefs. And then THOSE beliefs are “imposed” on that culture/society.
I don't want to put words in your mouth, but the implication of what you're saying is that the only way to defeat militant Islam is to push our country further away from being a secular republic and closer to a governmental system with religious aspects.
When did the ideal of a secular, pluralistic republic become unfashionable?
The same people who reject cretionism as science will reject Islamic dogma just as well. The ones who can be forced into compliance are the ones who would make good dhimmis.
IOW, there's no avoiding having someone else's religious beliefs imposed on us - except to voluntarily embrace yours?