Detailed examination of astrophysical constraints on the symmetry energy and the neutron skin of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mn>208</mml:mn></mml:mmultiscripts></mml:math> with minimal modeling assumptions

The symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283\ifmmode\pm\else\textpm\fi{}0.071$ fm for the neutron-skin thickness of $^{208}\mathrm{Pb}$, ${R}_{\mathrm{skin}}^{^{208}\mathrm{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106\ifmmode\pm\else\textpm\fi{}37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representation based on Gaussian processes to constrain the symmetry energy ${S}_{0}$, $L$, and ${R}_{\mathrm{skin}}^{^{208}\mathrm{Pb}}$ directly from observations of neutron stars with minimal modeling assumptions. The resulting astrophysical constraints from heavy pulsar masses, LIGO/Virgo, and NICER favor smaller values of the neutron skin and $L$, as well as negative symmetry incompressibilities. Combining astrophysical data with chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$) and PREX-II constraints yields ${S}_{0}=33.{0}_{\ensuremath{-}1.8}^{+2.0}$ MeV, $L={53}_{\ensuremath{-}15}^{+14}$ MeV, and ${R}_{\mathrm{skin}}^{^{208}\mathrm{Pb}}=0.{17}_{\ensuremath{-}0.04}^{+0.04}$ fm. We also examine the consistency of several individual $\ensuremath{\chi}\mathrm{EFT}$ calculations with astrophysical observations and terrestrial experiments. We find that there is only mild tension between $\ensuremath{\chi}\mathrm{EFT}$, astrophysical data, and PREX-II's ${R}_{\mathrm{skin}}^{^{208}\mathrm{Pb}}$ measurement ($p$ value $=12.3%$) and that there is excellent agreement between $\ensuremath{\chi}\mathrm{EFT}$, astrophysical data, and other nuclear experiments.