Put 1 cup of the flour in a shallow bowl and set aside. In another bowl, whisk together the remaining 1 cup flour, the beer and Cajun seasoning. Let the batter sit for 5 minutes.
Pour enough oil into a 3- to 4-quart saucepan to reach a depth of 2 inches. Heat the oil over medium-high heat until a deep frying/candy thermometer clipped to the side of the pan without touching the bottom registers 350 degrees F.
Dredge the pickles and peppers in the flour, shaking off any excess. Dip into the batter and coat completely, then transfer to the oil. Fry, turning with tongs, until golden brown on all sides, 2 to 3 minutes total. Drain on paper towels and serve.