There is a radial force. There is also an axial force, since the compressor pushes the air the force is in the opposite direction from the air flow. The sum of all the blade axial blade forces is transmitted down the rotor to the thrust bearing. Axial compressors often have larger active then inactive thrust bearings
Do a vector diagram of all the forces acting on the blade. I still think that the net force will be a high percentage radial but I don't discount the axial and lateral forces either. Neither do the blade designers.
