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Polarization plays an important role in various time-domain astrophysics to understand the magnetic fields, geometry, and environments of spatially unresolved variable sources. In this paper we present the results of laboratory and on-sky testing of a novel dual-beam, dual-camera optical imaging polarimeter (MOPTOP) exploiting high sensitivity, low-noise CMOS technology and designed to monitor variable and transient sources with low systematic errors and high sensitivity. We present a data reduction algorithm that corrects for sensitivity variations between the cameras on a source-by-source basis. Using our data reduction algorithm, we show that our dual-beam, dual-camera technique delivers the benefits of low and stable instrumental polarization ($<0.05$\% for lab data and $<0.25$\% for on sky data) and high throughput while avoiding the additional sky brightness and image overlap problems associated with dual-beam, single-camera polarimeters.