  In this work we investigate neutron stars (NS) in $f(\mathcal{R,T})$ gravity
for the case $R+2\lambda\mathcal{T}$, $\mathcal{R}$ is the Ricci scalar and
$\mathcal{T}$ the trace of the energy-momentum tensor. The hydrostatic
equilibrium equations are solved considering realistic equations of state
(EsoS). The NS masses and radii obtained are subject to a joint constrain from
massive pulsars and the event GW170817. The parameter $\lambda$ needs to be
negative as in previous NS studies, however we found a minimum value for it.
The value should be $|\lambda|\lesssim0.02$ and the reason for so small value
in comparison with previous ones obtained with simpler EsoS is due to the
existence of the NS crust. The pressure in theory of gravity depends on the
inverse of the sound velocity $v_s$. Since, $v_s$ is low in the crust,
$|\lambda|$ need to be very small. We found that the increment in the star mass
is less than $1\%$, much smaller than previous ones obtained not considering
the realistic stellar structure, and the star radius cannot become larger, its
changes compared to GR is less than $3.6\%$ in all cases. The finding that
using several relativistic and non-relativistic models the variation on the NS
mass and radius are almost the same for all the EsoS, manifests that our
results are insensitive to the high density part of the EsoS. It confirms that
stellar mass and radii changes depend only on crust, where the EoS is
essentially the same for all the models. The NS crust effect implying very
small values of $|\lambda|$ does not depend on the theory's function chosen,
since for any other one the hydrostatic equilibrium equation would always have
the dependence $1/v_s$. Finally, we highlight that our results indicate that
conclusions obtained from NS studies done in modified theories of gravity
without using realistic EsoS that describe correctly the NS interior can be
unreliable.
