Curtis N wrote in post #15423959
The camera uses distance information from the lens as part of its calculations for flash output in E-TTL mode (when using direct flash). Since it doesn't know about the polarizer, it's going to underexpose a little.
E-TTL isn't perfect. Crank up your FEC and drive on.
Sounds like a plausible explanation to me...
I tried to duplicate the OP's problem with my 60D, the onboard flash and a CPL shot at 0 and 90 degrees, in Av, Tv, M and Green Rectangle.
I got no lighting differences from 0 and 90 degrees, all shots perfectly lit. So there goes my theory about polarized light...
Av and Tv used the flash as fill (much longer speed or open aperture).
Green Rectangle and P recorded properly in all shots.
However, my distance to the subject was about 4 ft, so maybe at larger distances, Curtis' theory may come true.