The 2-hole horizontally polarized diffracted intensity and phase patterns are identical to the unpolarized case, producing the same intensity interference pattern:
And the polarization is everywhere horizontal:
The 2-hole vertically polarized diffracted intensity and phase patterns are also identical to the unpolarized case:
And the polarization is everywhere vertical:
You'll have to take my word again that linear polarization of any orientation at both holes (as long as it is the same orientation at both) produces the usual scalar diffraction patterns. But what about a different polarization at each hole...?