  We inspect the possibility that neutron star interiors are a mixture of
ordinary matter and mirror dark matter. This is a scenario that can be
naturally envisaged according to well studied accretion mechanisms, including
the Bondi-Hoyle one. We show that the inclusion of mirror dark matter in
neutron star models lowers the maximum neutron star mass for a given equation
of state, and that it decreases the tidal deformability of a given neutron
star. These general features imply that, given an equation of state, one can
constrain the maximum viable amount of mirror dark matter in neutron stars in
order to consistently fulfill existing maximum mass and tidal deformability
constraints. Conversely, using tidal deformability measurements to rule out
equations of state requires making assumptions on the amount of mirror dark
matter contained in neutron stars. Finally, the presence of mirror dark matter
also modifies the universal relation that links the tidal deformability of a
neutron star to its compactness. Therefore, caution is mandatory when
considering exotic models, such as the ones discussed in this paper.
