The spectral line polarization produced by optically pumped atoms contains a wealth of information on the thermal and magnetic structure of a variety of astrophysical plasmas, including that of the solar atmosphere. A correct decoding of such information from the observed Stokes profiles requires a clear understanding of the effects that radiatively induced quantum interference (or coherence) between pairs of magnetic sublevels produces on these observables, in the absence of and in the presence of magnetic fields of arbitrary strength. Here we present a detailed theoretical investigation of the role of coherence between pairs of sublevels pertaining to different fine-structure J-levels, clarifying when it can be neglected for facilitating the modeling of the linear polarization produced by scattering processes in spectral lines. To this end, we apply the quantum theory of spectral line polarization and calculate the linear polarization patterns of the radiation scattered at 90° by a slab of stellar atmospheric plasma, both taking into account and neglecting the above-mentioned quantum interference. Particular attention is given to the 2 S - 2 P, 5 S - 5 P, and 3 P - 3 S multiplets. We point out the observational signatures of this kind of interference and analyze its sensitivity to the energy separation between the interfering levels, to the amount of emissivity in the background continuum radiation, to lower-level polarization, and to the presence of a magnetic field. Some interesting applications to the following spectral lines are also presented: Ca II H and K, Mg II h and k, Na I D1 and D2, the Ba II 4554 Å and 4934 Å resonance lines, the Cr I triplet at 5207 Å, the O I triplet at 7773 Å, the Mg I b-lines, and the Hα and Lyα lines of H I.