  Galaxy surveys provide one of the best ways to constrain the theory of
gravity at cosmological scales. They can be used to constrain the two
gravitational potentials encoding time, $\Psi$, and spatial, $\Phi$,
distortions, which are exactly equal at late time within general relativity.
Hence, any small variation leading to a nonzero anisotropic stress, i.e. a
difference between these potentials, would be an indication for modified
gravity. Current analyses usually consider gravitational lensing and
redshift-space distortions to constrain the anisotropic stress, but these rely
on certain assumptions like the validity of the weak equivalence principle, and
a specific time evolution of the functions encoding deviations from general
relativity. In this work, we propose a reparametrization of the gravitational
lensing observable, together with the use of the relativistic dipole of the
correlation function of galaxies to directly measure the anisotropic stress
with a minimum amount of assumptions. We consider the future Legacy Survey of
Space and Time of the Vera C. Rubin Observatory and the future Square Kilometer
Array, and show that combining gravitational lensing and gravitational redshift
with the proposed approach we will achieve model-independent constraints on the
anisotropic stress at the level of $\sim 20\,\%$.
