Boy, oh boy. Where do I start with this? As others have said, not all religious people are afraid.
I'm religious. Not afraid.
I also disagree that the opposition comes from an underlying fear that their premise is flawed, foolish. Again, as other posters have pointed out, fear is an emotion. The visceral fear of "opposers", "athiests" has to do with a genuine, illogical fear. There could be a fear that their reasoning is controlled by Satan, even, and that their words have the power to suck the unsuspecting in to perdition. Terrifying!
I believe the fundamentalist's (the subset of the religious who are afraid) primary fear is loss of traditional values. I think this is the chief draw to fundamentalist religions, especially in this era of change. There is a tendency to take complex issues and oversimplify them. Entire sects have been built on oversimplifying and creating a false dichotomy. Take the militarization of a term like jihad, for instance. Equally false is to demonize all of Islam by the Christian West.
I got a whole new perspective on the issues, and a greater appreciation for the strength of the fundamentalist's fear in Karen's Armstrong's book, the Battle for God. Armstrong's argument, to calm the fundamentalist, is to first allay their fears.
Kind of like how one approaches a cultist, come to think of it.
Which brings me back to your original question. It oversimplifies the issue by lumping all religious in to the fear pot. But, modified, your question has merit. Why are fundamentalists afraid of athiests? They are afraid that the athiests will grab our society by the throat and drag it in to an unrecognizable future. With Satan's blessing.
By the way, I am afraid of people who are ruled by emotion. They are unpredictable. They panic. They frantically claw their neighbours in their efforts to return to safety.
Softly, softly catchee monkey.