  Theories of gravity with auxiliary fields are of particular interest since
they are able to circumvent Lovelock's theorem while avoiding to introduce new
degrees of freedom. This type of theories introduces derivatives of the
stress-energy tensor in the modified Einstein equation. This peculiar structure
of the field equations was shown to lead to spacetime singularities on the
surface of stars. Here we focus on yet another problem afflicting gravity
theories with auxiliary field. We show that such theories introduce deviations
to the Standard Model unless one severely constrains the parameters of the
theory, preventing them to produce significant phenomenology at large scales.
We first consider the specific case of Palatini $f({\cal R})$ gravity, to
clarify the results previously obtained in arXiv:astro-ph/0308111. We show that
the matter fields satisfy the Standard Model field equations which reduce to
those predicted by General Relativity in the local frame only at tree level,
whereas at higher orders in perturbation theory they are affected by
corrections that percolate from the gravity sector regardless of the specific
$f({\cal R})$ model considered. Finally, we show that this is a more general
issue affecting theories with auxiliary fields connected to the same terms
responsible for the appearance of surface singularities.
