  We study scalar cosmological perturbations in $f(R, T)$ modified gravity
theories being $T$ the trace of the energy-momentum tensor. We provide detailed
equations for the matter energy density contrast. We solve then numerically to
promote a comparison with available large scale structure (LSS) formation
observational data on $f \sigma_8$ and also addressing the $S_8$ tension. We
identify $f(R,T)$ models that lead either to growth enhancement or suppression.
Since recent results in the literature indicate a preference for the latter
feature, this type of analysis is quite useful to select viable modifications
of gravity. We studied class of such $f(R,T)$ models are either ruled out or
severely restricted.
