  We present polarisation properties at $1.4\,$GHz of two separate
extragalactic source populations: passive quiescent galaxies and luminous
quasar-like galaxies. We use data from the {\it Wide-Field Infrared Survey
Explorer} data to determine the host galaxy population of the polarised
extragalactic radio sources. The quiescent galaxies have higher percentage
polarisation, smaller radio linear size, and $1.4\,$GHz luminosity of
$6\times10^{21}<L_{\rm 1.4}<7\times10^{25}\,$W Hz$^{-1}$, while the quasar-like
galaxies have smaller percentage polarisation, larger radio linear size at
radio wavelengths, and a $1.4\,$GHz luminosity of $9\times10^{23}<L_{\rm
1.4}<7\times10^{28}\,$W Hz$^{-1}$, suggesting that the environment of the
quasar-like galaxies is responsible for the lower percentage polarisation. Our
results confirm previous studies that found an inverse correlation between
percentage polarisation and total flux density at $1.4\,$GHz. We suggest that
the population change between the polarised extragalactic radio sources is the
origin of this inverse correlation and suggest a cosmic evolution of the space
density of quiescent galaxies. Finally, we find that the extragalactic
contributions to the rotation measures (RMs) of the nearby passive galaxies and
the distant quasar-like galaxies are different. After accounting for the RM
contributions by cosmological large-scale structure and intervening Mg\,{II}
absorbers we show that the distribution of intrinsic RMs of the distant
quasar-like sources is at most four times as wide as the RM distribution of the
nearby quiescent galaxies, if the distribution of intrinsic RMs of the
WISE-Star sources itself is at least several rad m$^{-2}$ wide.
