A modular dovetail rail clamping assembly includes a polymer body and a metal fixed clamp component. A threaded fastener extends through the body and into the fixed clamp component to draw the fixed clamp component into engagement with the body. The fixed clamp component and the body have mating longitudinal ridge and groove structures which rigidly fix alignment of the fixed clamp component relative to the body when assembled. A metal movable clamp component opposes the fixed clamp. A threaded clamping fastener extends through the movable clamp component and the body, and is received into the fixed clamp component to draw the movable clamp component into engagement with the body. A removable, reversible crossbar extends transversely across the body between the fixed clamp component and the movable clamp component.