There seems to be two parts of the question, regarding chromatic spectrum, and polarization.
A polychromatic beam of X-rays can be dispersed by diffraction from a crystal, in a similar way to the rainbow spectral components of visible light being angularly dispersed by refraction through a prism. X-ray instruments often use two reflections from silicon (or similar crystals) to first disperse, then select a monochromatic wavelength for an experiment.
X-ray polarization can be used for example to image magnetic structures by obtaining the difference between two images created with opposite circular polarization. See, e.g., X-ray magnetic circular dichroism. This type of measurement can be done with visible light also.
to my knowledge the only polarizing principle in the x-ray domian is the Compton scatter at 90°. This geometry acts like the Brewster angle in visible optics, but the result does not depend on the x-ray wavelength/photon energy.
So we will not get 'colourful' 'pattern', which can be used as some kind of 'monochromatic' radiation. Apart from the 'polarization process' the x-ray photon energy is unfortunately lowered due to the Compton scatter events.
So this set up is more an 'analyzer' rather than an x-ray polarizer.
Significant Compton scatter will show up above some keV to some 10keV (Z-dependent).