We present average R-band optopolarimetric data, as well as variability parameters, from the first and second RoboPol observing season. We investigate whether gamma- ray–loud and gamma-ray–quiet blazars exhibit systematic differences in their optical polarization properties. We find that gamma-ray–loud blazars have a systematically higher polarization fraction (0.092) than gamma-ray–quiet blazars (0.031), with the hypothesis of the two samples being drawn from the same distribution of polarization fractions being rejected at the 3{sigma} level. We have not found any evidence that this discrepancy is related to differences in the redshift distribution, rest-frame R-band lu- minosity density, or the source classification. The median polarization fraction versus synchrotron-peak-frequency plot shows an envelope implying that high synchrotron- peaked sources have a smaller range of median polarization fractions concentrated around lower values. Our gamma-ray–quiet sources show similar median polarization fractions although they are all low synchrotron-peaked. We also find that the random- ness of the polarization angle depends on the synchrotron peak frequency. For high synchrotron-peaked sources it tends to concentrate around preferred directions while for low synchrotron-peaked sources it is more variable and less likely to have a pre- ferred direction. We propose a scenario which mediates efficient particle acceleration in shocks and increases the helical B-field component immediately downstream of the shock.