Materials do make a difference - how much depends on the wavelength and 'definition' (the ability to discriminate what is the target vs what is the background, at any given range) of the radar setup.
The best example I can think of is using a radar to 'see' through a wooden wall. Depending on the wavelength you may be able to discriminate objects on the other side of the wall, in particular objects with high radar signatures (metal objects for example). If the radar and wavelength is the sort that can detect moisture, you may be able to detect the outlines of people on the other side of the wall.
On the other hand, the same radar that can see through a wooden wall will not be able to see through a solid metal wall, and the radar signature of the metal wall will completely blank the radar screen. Even a thin layer of metal like aluminum foil will block nearly all radars.
However, wood is not 100% transparent to radio/radar waves, which means that radars can detect wooden objects, though at significantly shorter ranges than metal objects of the same shape and size. Also, metal objects outside the wooden aircraft structure (like propellers, gun barrels, exhaust manifolds, etc) or inside the wooden aircraft structure (engines, landing gear, bomb gear, even screws and other fasteners, etc) will reflect the radar waves.