So are you asking why your book says what it does -- why it says that this caused the radicals to take control and to separate church and state? I'm not clear... Let me know if I've misunderstood.
The Dreyfus Affair did these things because it discredited the the people who liked things the old way. It proved, in many people's minds, that the old system was corrupt and needed to be changed in a fundamental way like the radicals wanted. So this event really made clear that true change (not just incremental change) was needed.
Is that what you're asking?