Stir together buttermilk and egg. Combine cracker crumbs, flour, and salt. Dip okra pieces in buttermilk mixture; dredge in cracker crumb mixture.
Pour oil to a depth of 2 inches into a Dutch oven or cast-iron skillet; heat to 375°. Fry okra, in 3 batches, 2 minutes or until golden, turning once. Drain on paper towels.