  Non-VLBI measurements of Faraday rotation at mm wavelengths have been used to
constrain mass accretion rates ($\mdot$) onto supermassive black holes in the
centre of the Milky Way and in the centre of M87. We constructed general
relativistic magnetohydrodynamics models for these sources that qualitatively
well describe their spectra and radio/mm images invoking a coupled jet-disk
system. Using general relativistic polarized radiative transfer, we now also
model the observed mm rotation measure (RM) of M87. The models are tied to the
observed radio flux, however, electron temperature and accretion rate are
degenerate parameters and are allowed to vary. For the inferred low viewing
angles of the M87 jet, the RM is low even as the black hole $\mdot$ increases
by a factor of $\simeq100$. In jet-dominated models, the observed linear
polarization is produced in the forward-jet, while the dense accretion disk
depolarizes the bulk of the near-horizon scale emission which originates in the
counter-jet. In the jet-dominated models, with increasing $\mdot$ and
increasing Faraday optical depth one is progressively sensitive only to
polarized emission in the forward-jet, keeping the measured RM relatively
constant. The jet-dominated model reproduces a low net-polarization of
$\simeq1$ per cent and RMs in agreement with observed values due to Faraday
depolarization, however, with $\mdot$ much larger than the previously inferred
limit of $9\times10^{-4}\,\mdotu$. All jet-dominated models produce much higher
RMs for inclination angles $i\gtrsim30^\circ$, where the line-of-sight passes
through the accretion flow, thereby providing independent constraints on the
viewing geometry of the M87 jet.
