Line scattering polarization can be strongly affected by Rayleigh scattering at neutral hydrogen and Thomson scattering at free electrons. Often a depolarization of the continuum results, but the Doppler redistribution produced by the continuum scatterers, which are light (hence, fast), induces more complex interactions between the polarization in spectral lines and in the continuum. Here we formulate and solve the radiative transfer problem of scattering line polarization with non-coherent continuum scattering consistently. The problem is formulated within the spherical tensor representation of atomic and light polarization. The numerical method of solution is a generalization of the Accelerated Lambda Iteration that is applied to both the atomic system and the radiation field. We show that the redistribution of the spectral line radiation due to the non-coherence of the continuum scattering may modify the shape of the emergent fractional linear polarization patterns significantly, even yielding polarization signals above the continuum level in intrinsically unpolarizable lines.