I think that one of the fundamental challenges that surrounds Islamic fundamentalism is how to reconcile itself with the growth of liberal democracy. The worldwide spread of liberal democracy is at odds with Islamic fundamentalism: "Western and Islamic visions of the state, the individual and society are not only divergent, they are often totally at odds." As more nations embrace globalization and the liberal democratic setting that facilitates it, Islamic fundamentalism is challenged. Its presentation of the world is basically at odds with an emergent liberal and secular world community.
The result is that Islamic fundamentalism tends to marginalize itself. Islamic fundamentalism's challenge is being unable to bring more people from divergent backgrounds into it and presenting itself as a narrative that encompasses more voices as a plausible alternative. All fundamentalism faces the same challenge. Given the claims that Islamic fundamentalism asserts, its case and challenges are more visible in this regard.
This reveals another challenge that Islamic fundamentalism has to address. The movement itself is associated with terrorism and fanaticism. Certainly, all brands of fundamentalism presents itself more akin to embracing zealotry. Yet, with the emphasis on a worldwide "war on terror," Islamic fundamentalism is closely aligned with terrorism in the minds of many people. This fear casts a pall. It makes people automatically distrustful and causes them to strike a position of reticence and resistance. Once again, this filters into the idea that Islamic fundamentalism paints itself in a corner where a wider embrace is near impossible.
I think that another challenge that Islamic fundamentalism faces is internally. As a whole, Islam is a very peaceful and compassionate religion. A religion that "embraces one fifth of the world's population" is reflective of something quite tolerant and filled with openness. This vision of Islam is at odds with the picture painted by Islamic fundamentalism. On some level, the religion itself is antithetical to the ideas articulated by those who embrace its fundamentalist zeal. Most fundamentalists in all religion do not speak for the majority of the religion. The extreme nature of fundamentalism is not reflective of a moderate mainstream of followers. This is evident in Islam, a religion that intrinsically challenges the vision that its fundamentalist elements wish to use. Over time, this can prove to be challenging as fundamentalism seeks to draw out a picture that might not necessarily be so.