I found a pair of polarizing "3D glasses" lying around, and tried to look at myself in the mirror while wearing them.
To my utter confusion, when closing the left eye and only looking through the right eye, I could not see the right eye in the mirror. The light could not pass through the same polarized lens twice. (I could, however, see the closed left eye clearly.)
I would expect the opposite to be true, as light going out the right lens with polarization X and coming back in with the same polarization X should pass through unaffected.
Best Answer
See the Wiki article on Polarized 3D glasses. Most likely, you have a pair of circularly polarized glasses. The mirror reverses the circular polarization.
The article on Circular polarization does it better than I would be likely to achieve in less than an hour or two. Or Hyperphysics, or Google.