You're right that for perfectly vertical reflection, the polarization doesn't matter, but you're unlikely to exactly hit that. For angles between 0 and 90 degrees, light polarized parallel to the surface is always reflected better. If you perfectly hit Brewster's angle https://en.wikipedia.org/wiki/Brewster%27s_angle the light will be completely linearly polarized, but that is equally unlikely. So in general you're going to get mixed polarization that's slightly biased in one direction.