A833 rattles with new clutch and throw out

This post is accurate in my opinion.

Once the input bushing is out of alignment or has offset due to failure or massive wear, it allows the clutch to be engaged in an offset relative to center of crank. This creates vibration relative to RPM w/o the car being in gear. Although there is considerably more vibration and rattle when disengaged (clutch petal in) due to wallow offset rattle.

When I was young I put a 4 sp in a 318 with no pilot bushing (yeap dumb). It displayed the above symptoms.

If the bushing is off center somehow, or not there, the input shaft will be vibrating whether the clutch is engaged or not.