I think that depends on what type of foot brace your have chosen to mount. Simple "keeper" braces can be screwed to a wood block inside. I would recommend a hardwood to hold good wood screws well. If you plan to have a bolt through to a recessed nut on the back of the wood, I think a softer wood would be fine. I usually use hardwood since I never know how hard someone is going to push on their foot braces to adjust their position.
More complicated foot braces require more than a simple block of wood, since some may require bolts through from the back which thread into pre-existing mounting holes on the foot brace itself. On the current project I am installing the Seal Line rudder system foot braces that can be retrofitted for rudder later. I have to glue a piece of hardwood into the hull to which another piece of hardwood will be attached with bolts. This is because the brackets require a bolt from the back. This way the customer will be able to remove the top portion to remove the foot brace.