  Recent lattice QCD studies at vanishing density exhibit the parity-doubling
structure for the low-lying baryons around the chiral crossover temperature.
This finding is likely an imprint of the chiral symmetry restoration in the
baryonic sector of QCD, and is expected to occur also in cold dense matter,
which makes it of major relevance for compact stars. By contrast, typical
effective models for compact star matter embody chiral physics solely in the
deconfined sector, with quarks as degrees of freedom. In this contribution, we
present a description of QCD matter based on the effective hybrid
quark-meson-nucleon model. Its characteristic feature is that, under
neutron-star conditions, the chiral symmetry is restored in a first-order phase
transition deep in the hadronic phase, before the deconfinement of quarks takes
place. We discuss the implications of the parity doubling of baryons on the
mass-radius relation for compact stars obtained in accordance with the modern
constraints on the mass from PSR J0348+0432, the compactness from GW170817, as
well as the direct URCA process threshold. We show that the existence of
high-mass stars might not necessarily signal the deconfinement of quarks.
