Because my character interacts with the physics system, I need to move my character in FixedUpdate. Unfortunately, this causes all transforms constrained by the animation rig to jitter when moving.
What is the recommended approach to character movement when using Animation Rigging?
Have you tried setting the update mode on your Animator to Animate Physics?
This option will make your animation evaluate in fixed update time rather than in the normal game logic update loop.
You can refer to the following page for more information on Unity order of execution.