  Fast radio bursts (FRBs) display a confounding variety of burst properties
and host galaxy associations. Repeating FRBs offer insight into the FRB
population by enabling spectral, temporal and polarimetric properties to be
tracked over time. Here, we report on the polarized observations of 12
repeating sources using multi-year monitoring with the Canadian Hydrogen
Intensity Mapping Experiment (CHIME) over 400-800 MHz. We observe significant
RM variations from many sources in our sample, including RM changes of several
hundred $\rm{rad\, m^{-2}}$ over month timescales from FRBs 20181119A,
20190303A and 20190417A, and more modest RM variability ($\rm{\Delta RM
\lesssim}$ few tens rad m$^{-2}$) from FRBs 20181030A, 20190208A, 20190213B and
20190117A over equivalent timescales. Several repeaters display a frequency
dependent degree of linear polarization that is consistent with depolarization
via scattering. Combining our measurements of RM variations with equivalent
constraints on DM variability, we estimate the average line-of-sight magnetic
field strength in the local environment of each repeater. In general, repeating
FRBs display RM variations that are more prevalent/extreme than those seen from
radio pulsars in the Milky Way and the Magellanic Clouds, suggesting repeating
FRBs and pulsars occupy distinct magneto-ionic environments.
