Thomson scattering on the electrons does not produce any circular polarization? All references on CMB polarization has this statement as if it is a trivial fact. But I have to admit that I completely don't understand what this sentence is telling us.
 A: Unpolarised light can be regarded as an equal mixture of perpendicular polarisations with random phases. The perpendicular polarisations cause perpendicular oscillations in an electron which then re-radiates in all directions except along the axis of an oscillation. The resultant scattered light is partially linearly polarised (because the two polarisation components, although still having a random phase relationship, are not scattered equally in all directions) or completely linearly polarised if observed at right angles to the incoming radiation.
For example, see the animations here.
To get circular (or elliptical) polarisation would require a fixed phase relationship between the two polarisation components of the light that is being scattered. The only way to arrange this is if the light that is being scattered is already circularly (or elliptically) polarised and even then, the scattered light has a reduced circular polarisation unless observing in the exact forward or back-scattered direction.
