There are many types of thread-on rotating polarizing filter designs. There are also many different types of lens shades (or hoods).
Because polarizers are 2-piece laminated filters (two pieces of optical glass with a polarizing foil laminated in between), they are naturally thicker than ordinary filters. The necessity of a rotating mount also normally increases the filter mount thickness and width.
Due to their inherent increased thickness relative to ordinary filters, some polarizers are designed to be oversized in width to avoid vignetting when attached to shorter focal length lenses. This may eliminate the use of certain lens shade designs or the use of any lens shade at all.
As a means of reducing thickness, some polarizers are mounted in "slim" mounts without the usual double (female front) threads. A filter lacking double threads will eliminate the use of some lens hoods designed to attach via front threads.
So, due to a specific polarizer's thickness, a lens shade may be extended too far and vignette. Due to a specific polarizer's intentionally oversized width, a shade may not be attachable at all. Due to the lack of front threads in "slim" polarizers, some lens shades are not usable.
Also, due to the need to rotate a polarizer for the desired effect, many lens shades make it inconvenient to operate a polarizer. In many cases where a polarizer is used, it is more convenient and practical to simply flag the lens for flare control. There are some filter holder systems which are specifically designed to
combine a polarizer with a lens shade or a flag may attach to the filter holder for shading. You may find that to be the exception rather than the rule, however.
It should not be assumed that any polarizer and lens shade combination will work together conveniently or at all. This needs to be checked and confirmed before purchasing. Failure to do so lies with the purchaser; all blame shifting and accusations of manufacturer error, stupidity, or insanity notwithstanding.
It should also be noted that with one exception, all of the Mamiya/Phase One lenses which are co-branded with Schneider are actually Mamiya/Phase One lens designs and are not designed or manufactured by Schneider. For the reasons already stated, there is no reason to assume that a polarizer of any brand is going to just fit or work with a given lens hood in the manner you would like or at all.