Reproduction:
  1. create 3d object cube
  2. add VRC_Pickup script
  3. add UdonBehavior
  4. Set UdonBehavior.synchronizePosition = true
  5. Add simple Udon script to the UdonBehavior that runs the equivalent of
Interact() { GetComponent<RigidBody>().isKinematic = true }
Expected:
When you pick up the cube in game and drop it, it'll remain in place as it's kinematic.
Actual:
Cube remains non-kinematic and falls to the floor.
If you unset Synchronize Position, toggling isKinematic behaves as expected, for an otherwise identical setup.