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 degrees by a slab of stellar atmospheric plasma, both taking into account and neglecting the above-mentioned quantum interference. Particular attention is given to the S-2 - P-2, S-5 - P-5, and P-3 - S-3 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: CaII H and K, Mg II h and k, Na I D-1 and D-2, the BaII 4554 angstrom and 4934 angstrom resonance lines, the Cr I triplet at 5207 angstrom, the OI triplet at 7773 angstrom, the Mg I b-lines, and the H alpha and Ly alpha lines of HI.