Which joints are set to non-kinematic here? In my experience, the wobbling can happen when running with the Root or Waist set to non-kinematic. I recommend keeping Root and Waist set to IsKinematic = true.
This is because the HumanoidRootPart is the main thing that moves roblox characters. The rest of the body just “gets dragged along”. The UpperTorso is a relatively heavy mass, so if the HRP is whipping it around rapidly the character body will flop around more. Conversely, if you keep the Root and Waist kinematic, the only parts flopping around will be the head, arms, and legs.
In the demo place, I made only the arm joints non-kinematic when walking around, which ends up being much more stable. Also, using the ControllerManager gives even more stability.