Pour the oil into a large heavy-bottomed pot fitted with a deep-frying thermometer.
Combine the mozzarella, cream cheese, garlic salt and crushed red pepper in a food processor. Pulse until a thick paste is formed, about 30 seconds. Set aside.
On a lightly floured surface, roll the pizza dough to form a 16-by-12-inch rectangle. Use a 3-inch round cutter to cut out 10 to 12 rounds of dough. Use your fingertips to gently stretch each round of dough into a 4-inch circle. Top a round of dough (slightly off-center) with 1 heaping teaspoon of the cheese mixture and 1 teaspoon crabmeat. Fold the dough in half over the filling to create a half-moon. Press the edges together to seal the pocket and crimp with the prongs of a fork. (See Cook's Note.) Repeat this process with the remaining circles and filling.
Preheat the vegetable oil to 350 degrees F and line a plate with paper towels.
Working in batches, carefully lay the pizza pockets in the hot oil. Fry until deeply golden brown, 1 to 1 1/2 minute on each side. Remove from the hot oil to the lined plate to cool slightly.
Garnish with fresh parsley.
If you want extra protection from the pockets opening while frying, use a little water on the edges before sealing with a fork.