  The star formation and gas content of satellite galaxies around the Milky Way
(MW) and Andromeda (M31) are depleted relative to more isolated galaxies in the
Local Group (LG) at fixed stellar mass. We explore the environmental regulation
of gas content and quenching of star formation in $z=0$ galaxies at
$M*=10^{5-10}\rm{M}_{\odot}$ around 14 MW-mass hosts from the FIRE-2
simulations. Lower-mass satellites ($M*\lesssim10^7\rm{M}_{\odot}$) are mostly
quiescent and higher-mass satellites ($M*\gtrsim10^8\rm{M}_{\odot}$) are mostly
star-forming, with intermediate-mass satellites
($M*\approx10^{7-8}\rm{M}_{\odot}$) split roughly equally between quiescent and
star-forming. Hosts with more gas in their circumgalactic medium have a higher
quiescent fraction of massive satellites ($M*=10^{8-9}\rm{M}_{\odot}$). We find
no significant dependence on isolated versus paired (LG-like) host
environments, and the quiescent fractions of satellites around MW-mass and
LMC-mass hosts from the FIRE-2 simulations are remarkably similar.
Environmental effects that lead to quenching can also occur as preprocessing in
low-mass groups prior to MW infall. Lower-mass satellites typically quenched
before MW infall as central galaxies or rapidly during infall into a low-mass
group or a MW-mass galaxy. Most intermediate- to high-mass quiescent satellites
have experienced $\geq1-2$ pericentre passages ($\approx2.5-5$ Gyr) within a
MW-mass halo. Most galaxies with $M*\gtrsim10^{6.5}\rm{M}_{\odot}$ did not
quench before falling into a host, indicating a possible upper mass limit for
isolated quenching. The simulations reproduce the average trend in the LG
quiescent fraction across the full range of satellite stellar masses. Though
the simulations are consistent with the SAGA survey's quiescent fraction at
$M*\gtrsim10^8\rm{M}_{\odot}$, they do not generally reproduce SAGA's turnover
at lower masses.
