  The $f(R,T)$ gravity is a model whose action contains an arbitrary function
of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. We
consider the separable model $f (R, T ) = \chi(R) + \varphi(T )$ and shown
that, for perfect fluids, the dynamical equations are sufficient to determine
how $\varphi$ depends on $T$, independently of the matter state equation and
the geometry of space-time. Imposing the energy-momentum tensor conservation we
obtain that $\varphi$ must be linear in $T$. However, the $T$ dependence is
severely constrained using the full Will-Nordtvedt version of the parameterized
post-Newtonian (PPN) formalism. The result of the PPN analysis is discussed and
in addition it is shown that the diffeomorphism invariance of the matter action
imposes strong constraints on conservative versions of $f(R,T)$ gravity.
