In a crossed-beam experiment the total ionization cross section for the title systems has been investigated in the range 0.1\ensuremath{\leqslant}E (eV) \ensuremath{\leqslant}4 of collision energies. The population of the short-lived Ne**[(3p);J=3] state is produced by saturated optical pumping of the Ne*[(3s);J=2]\ensuremath{\leftrightarrow}Ne**[(3p);J=3] two-level system with a polarized laser beam, resulting in a well-determined distribution of the magnetic substrates |J,M〉 with respect to the relative velocity g. By measuring the ion yield in the scattering center at five different orientations of the laser polarization (linear and circular) with respect to g, the data can be analyzed in terms of pure-state total ionization cross sections Q3|M| corresponding to a single asymptotic state |J,M〉. The observed polarization effect at E=0.1 eV is Q3|M|=0,1/Q3|M|=3=2.5, which is in good agreement with the data of Bussert, T. Bregel, R. J. Allan, M. W. Ruf, and H. Hotop [Z. Phys. A 320, 105 (1985)] in the thermal energy range as obtained by analyzing the Penning electrons. This polarization effect decreases to a value of 1.4 for E>2 eV. The results are discussed in terms of semiclassical scattering calculations with an optical potential as input, using a model-potential approach for calculating both the real and the imaginary parts. For the autoionization width this results in a two-state \ensuremath{\Gamma}\ensuremath{\sigma}\ensuremath{'} and \ensuremath{\Gamma}\ensuremath{\pi}\ensuremath{'} basis for the \ensuremath{\sigma}\ensuremath{'} and \ensuremath{\pi}\ensuremath{'} orientations of the (2p)-1 hole, calculated in a one-electron orbital overlap approximation. The preference for the \ensuremath{\Omega}=0,1 states at E=0.1 eV indicates the correct relative scaling of these two ionization widths, leading to \ensuremath{\Gamma}\ensuremath{\sigma}\ensuremath{'}=79\ensuremath{\Gamma}\ensuremath{\pi}\ensuremath{'} at R=4.5a0. The observed energy dependence is due to the decrease of ``locking'' of the total angular momentum J to the internuclear axis R with increasing angular velocity \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, leading to the dynamical criterion \ensuremath{\omega}prec=4\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{} for the transition of a space-fixed to a body-fixed description of J. The semiclassical precession frequency \ensuremath{\omega}prec of J around R is related to the average \ensuremath{\Omega} splitting of the real part of the optical potential by \ensuremath{\omega}prec=〈\ensuremath{\Delta}V\ensuremath{\Omega},\ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}1〉/\ensuremath{\Elzxh}. With these assumptions we observe a good agreement between the experimental results and the semiclassical calculations. Finally, we discuss the validity of a semiclassical locking picture, with emphasis on the difference between locking of the angular momentum versus locking of the electron orbitals involved.