Relative physical laws and large-scale statistical properties do not depend on the chosen spatial origin. For a continuous deterministic galaxy velocity field, using the same relative-velocity rule from each origin forces additivity and hence a position-independent linear velocity gradient.
The traceless symmetric part of the galaxy velocity-gradient matrix changes shape without isotropic expansion. An antisymmetric part instead represents rigid rotation. A matrix proportional to the identity plus an antisymmetric matrix has no shear.

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