  We use cosmological hydrodynamical simulations to study the effect of
screened modified gravity models on the mass estimates of galaxy clusters. In
particular, we focus on two novel aspects: (i) we study modified gravity models
in which baryons and dark matter are coupled with different strengths to the
scalar field, and, (ii) we put the simulation results into the greater context
of a general screened-modified gravity parametrization. We have compared the
mass of clusters inferred via lensing versus the mass inferred via kinematical
measurements as a probe of violations of the equivalence principle at Mpc
scales. We find that estimates of cluster masses via X-ray observations is
mainly sensitive to the coupling between the scalar degree of freedom and
baryons - while the kinematical mass is mainly sensitive to the coupling to
dark matter. Therefore, the relation between the two mass estimates is a probe
of a possible non-universal coupling between the scalar field, the standard
model fields, and dark matter. Finally, we used observational data of kinetic,
thermal and lensing masses to place constraints on deviations from general
relativity on cluster scales for a general parametrization of screened modified
gravity theories which contains $f(R)$ and Symmetron models. We find that while
the kinematic mass can be used to place competitive constraints, using thermal
measurements is challenging as a potential non-thermal contribution is
degenerate with the imprint of modified gravity.
