Contrary to the stability astronomers typically expect from millisecond pulsars, the shape of PSR J1022+1001’s pulse profile is highly variable. The reason for this behavior is still not settled over 20 years after its discovery. This pulsar was observed for over 5 years with the Arecibo radio telescope as part of NANOGrav’s pulsar timing campaign. Like all NANOGrav timing observations, these data have undergone the state of the art polarization calibration procedure, and this pulsar’s calibrated pulse profile is still highly unstable. We present evidence that fitting a Mueller matrix to each observation can account for and remove this variability, producing a stable and reliable intensity profile. We also explore the effect of Mueller matrix template matching on the timing stability of this pulsar.