Within the films, it is consistent for them to cast shadows. They cast shadows throughout the OT. To remove the shadows in only one film would be an inconsistency.

Outside of that, they're clearly solid. You can never see through a lightsaber blade at any point in any of the films. An object casting light isn't going to create a shadow of itself. However, if you had a second light source being cast on the object it would create a shadow because it's blocking out the light from the second source.