  Ho\v{r}ava gravity breaks boost invariance in the gravitational sector by
introducing a preferred time foliation. The dynamics of this preferred slicing
is governed, in the low-energy limit suitable for most astrophysical
applications, by three dimensionless parameters $\alpha$, $\beta$ and
$\lambda$. The first two of these parameters are tightly bound by solar system
and gravitational wave propagation experiments, but $\lambda$ remains
relatively unconstrained ($0\leq\lambda\lesssim 0.01-0.1$). We restrict here to
the parameter space region defined by $\alpha=\beta=0$ (with $\lambda$ kept
generic), which in a previous paper we showed to be the only one where black
hole solutions are non-pathological at the universal horizon, and we focus on
possible violations of the strong equivalence principle in systems involving
neutron stars. We compute neutron star 'sensitivities', which parametrize
violations of the strong equivalence principle at the leading post-Newtonian
order, and find that they vanish identically, like in the black hole case, for
$\alpha=\beta=0$ and generic $\lambda\neq0$. This implies that no violations of
the strong equivalence principle (neither in the conservative sector nor in
gravitational wave fluxes) can occur at the leading post-Newtonian order in
binaries of compact objects, and that data from binary pulsars and
gravitational interferometers are unlikely to further constrain $\lambda$.
