  Within the covariant density functional theory of hypernuclear matter we
build a series of equations of state for hypernuclear compact stars, by
calibrating the coupling constants of the $\Xi$-hyperon to the experimental
binding energy of the single-$\Xi$ hypernuclei $^{15}_{\Xi^-}$C and
$^{12}_{\Xi^-}$Be. Coupling constants of the $\Lambda$-hyperon to nucleons have
been calibrated on a vast collection of experimental data on single
$\Lambda$-hypernuclei and we employ those values. Uncertainties on the
couplings of the $\Sigma$-hyperon to nuclear matter, due to lack of
experimental data, are accounted for by allowing for a wide variation of the
well depth of $\Sigma$ at rest in symmetric saturated nuclear matter. To
account for uncertainties in the nucleonic sector at densities much larger than
the saturation density, a rich collection of parametrizations is employed, some
of them in agreement with existing constraints from nuclear physics and
astrophysics. Neutron star properties are investigated with all these
calibrated equations of state. The effects of the presence of hyperons on the
radius, on the tidal deformability, on the moment of inertia, and on the
nucleonic direct Urca process are discussed. The sensitivity of the hyperonic
direct Urca processes to uncertainties in the nucleonic and hyperonic sectors
is also addressed. It is shown that the relative variations of the radius,
tidal deformability and moment of inertia from the values that characterize
purely nucleonic stars are linearly correlated with the strangeness fraction.
The maximum radius deviation, obtained for most massive neutron stars, is
$\approx 10\%$. The reduction of the maximum mass, triggered by nucleation of
strangeness, is estimated at $\approx 15 - 20\%$, out of which 5\% comes from
insufficient information on the $\Sigma$-hyperon interactions.
